Special Continuous Distribution (uppersixth science further new))

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Test your knowledge on the exponential distribution, its mean, and variance!

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YAKILI LMS

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Special Continuous Distribution (uppersixth science further new))


Froggy Jumps Special Continuous Distribution (uppersixth science further new))Online version Test your knowledge on the exponential distribution, its mean, and variance! by YAKILI LMS 1 What is the mean of an exponential distribution? a λ^2 b 1/λ c λ 2 What is the variance of an exponential distribution? a 1/λ b λ c 1/λ² 3 What does the parameter λ represent in the exponential distribution? a Rate of occurrence b Standard deviation c Mean value 4 The exponential distribution is often used to model what type of events? a Fixed intervals b Time until an event occurs c Discrete outcomes 5 Which of the following is a property of the exponential distribution? a Bimodal b Memoryless property c Symmetry 6 If λ = 2, what is the mean of the distribution? a 0.5 b 1 c 2 7 In the exponential distribution, what happens as λ increases? a Mean decreases b Skewness increases c Variance increases 8 What is the cumulative distribution function (CDF) of an exponential distribution? a 1 - e^(-λx) b e^(λx) c λx 9 Which distribution is a special case of the gamma distribution? a Binomial distribution b Exponential distribution c Normal distribution 10 What type of graph represents the probability density function (PDF) of an exponential distribution? a Bell curve b Flat line c Decreasing curve 11 What is the formula for the mean of a uniform distribution? a Mean = a + b b Mean = a - b c Mean = (a + b) / 2 12 What does 'a' represent in a uniform distribution? a 'a' is the mean value. b 'a' is the maximum value. c 'a' is the minimum value. 13 What is the variance formula for a uniform distribution? a Variance = (b + a)² / 12 b Variance = (b - a)² / 12 c Variance = (b - a) / 12 14 In a uniform distribution, what is the shape of the probability density function? a Bell-shaped b Triangular c Rectangular 15 What is the range of a uniform distribution defined by? a Range = a + b b Range = b - a c Range = a * b 16 If a uniform distribution has a = 2 and b = 8, what is the mean? a Mean = 5 b Mean = 6 c Mean = 4 17 What type of distribution is characterized by equal likelihood across its range? a Uniform distribution b Exponential distribution c Normal distribution 18 What is the variance if a uniform distribution has a = 1 and b = 5? a Variance = 3 b Variance = 2 c Variance = 1.33 19 Which of the following is NOT a property of a uniform distribution? a Symmetrical b Constant probability c Skewed 20 What is the cumulative distribution function (CDF) of a uniform distribution? a CDF = (b - x) / (b - a) b CDF = (x + a) / (b + a) c CDF = (x - a) / (b - a) 21 What shape does the normal distribution graph take? a Bell-shaped b Square-shaped c Triangular-shaped 22 What percentage of data falls within one standard deviation in a normal distribution? a 95% b 50% c 68% 23 What is the mean of a standard normal distribution? a 0 b 1 c 10 24 What does the area under the normal distribution curve represent? a Total probability b Mean value c Standard deviation 25 In a normal distribution, what is the relationship between mean, median, and mode? a Median is less b They are all equal c Mean is greater 26 What is the standard deviation of a standard normal distribution? a 1 b 0 c 2 27 What is the z-score for a value at the mean? a 1 b 0 c -1 28 Which of the following is a property of a normal distribution? a Skewed to the right b Symmetrical about the mean c Bimodal 29 What is the total area under the normal distribution curve? a 1 b 0 c 0.5 30 What is the significance of the empirical rule? a Calculates mean b Describes data distribution in normal curves c Determines variance 31 What shape does the normal distribution curve have? a Triangle-shaped b Square-shaped c Bell-shaped 32 What is the mean of a standard normal distribution? a 1 b 0 c 5 33 What percentage of data falls within one standard deviation in a normal distribution? a 50% b 68% c 95% 34 What does the area under the normal distribution curve represent? a Standard deviation b Total probability c Mean value 35 What is the standard deviation of a standard normal distribution? a 1 b 0 c 2 36 In a normal distribution, what is the relationship between mean, median, and mode? a They are all equal b Mean > Median > Mode c Mean < Median < Mode 37 What is the z-score in a normal distribution? a Number of standard deviations from the mean b The total area under the curve c The mean value 38 What is the total area under a normal distribution curve? a 0.5 b 0 c 1 39 Which of the following is NOT a property of the normal distribution? a Skewed to the left b Asymptotic to the x-axis c Symmetrical 40 What is the empirical rule in relation to normal distribution? a 60-80-100 rule b 68-95-99.7 rule c 50-75-90 rule 41 What is a probability density function (PDF)? a A function that only applies to normal distributions. b A function for discrete random variables. c A function that describes the likelihood of a continuous random variable. 42 What area under the PDF curve represents total probability? a 1 b 0 c 0.5 43 In a PDF, what does the height of the curve represent? a The actual value of the variable. b The mean of the distribution. c The likelihood of the variable taking a specific value. 44 Which of the following is true about a PDF? a It can exceed 1. b It must be a straight line. c It can never be negative. 45 What is the integral of a PDF over its entire range? a It varies based on the distribution. b 1 c 0 46 What is the purpose of a PDF? a To model the distribution of continuous random variables. b To find probabilities of specific outcomes. c To calculate the mean of discrete variables. 47 Which distribution is commonly associated with a PDF? a Normal distribution. b Poisson distribution. c Binomial distribution. 48 How do you find the probability of a range in a PDF? a Integrate the PDF over that range. b Add the values of the PDF at those points. c Multiply the heights of the PDF at those points. 49 What is a characteristic of a uniform PDF? a It decreases as you move away from the mean. b It has a constant height across its range. c It is always bell-shaped. 50 What does a higher peak in a PDF indicate? a A wider range of possible values. b A higher likelihood of values near that point. c A lower total probability.

Special Continuous Distribution (uppersixth science further new))

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Special Continuous Distribution (uppersixth science further new))Online version

by YAKILI LMS

What is the mean of an exponential distribution?

What is the variance of an exponential distribution?

What does the parameter λ represent in the exponential distribution?

The exponential distribution is often used to model what type of events?

Which of the following is a property of the exponential distribution?

If λ = 2, what is the mean of the distribution?

In the exponential distribution, what happens as λ increases?

What is the cumulative distribution function (CDF) of an exponential distribution?

Which distribution is a special case of the gamma distribution?

What type of graph represents the probability density function (PDF) of an exponential distribution?

What is the formula for the mean of a uniform distribution?

What does 'a' represent in a uniform distribution?

What is the variance formula for a uniform distribution?

In a uniform distribution, what is the shape of the probability density function?

What is the range of a uniform distribution defined by?

If a uniform distribution has a = 2 and b = 8, what is the mean?

What type of distribution is characterized by equal likelihood across its range?

What is the variance if a uniform distribution has a = 1 and b = 5?

Which of the following is NOT a property of a uniform distribution?

What is the cumulative distribution function (CDF) of a uniform distribution?

What shape does the normal distribution graph take?

What percentage of data falls within one standard deviation in a normal distribution?

What is the mean of a standard normal distribution?

What does the area under the normal distribution curve represent?

In a normal distribution, what is the relationship between mean, median, and mode?

What is the standard deviation of a standard normal distribution?

What is the z-score for a value at the mean?

Which of the following is a property of a normal distribution?

What is the total area under the normal distribution curve?

What is the significance of the empirical rule?

What shape does the normal distribution curve have?

What is the mean of a standard normal distribution?

What percentage of data falls within one standard deviation in a normal distribution?

What does the area under the normal distribution curve represent?

What is the standard deviation of a standard normal distribution?

In a normal distribution, what is the relationship between mean, median, and mode?

What is the z-score in a normal distribution?

What is the total area under a normal distribution curve?

Which of the following is NOT a property of the normal distribution?

What is the empirical rule in relation to normal distribution?

What is a probability density function (PDF)?

What area under the PDF curve represents total probability?

In a PDF, what does the height of the curve represent?

Which of the following is true about a PDF?

What is the integral of a PDF over its entire range?

What is the purpose of a PDF?

Which distribution is commonly associated with a PDF?

How do you find the probability of a range in a PDF?

What is a characteristic of a uniform PDF?

What does a higher peak in a PDF indicate?