A Continuous random variable has the uniform distribution on the interval [a, b]

Question

A Continuous random variable has the uniform distribution on the interval [a, b] if its probability density function f(x). Provides all probabilities for all x between Is bell-shaped between a and b. Is constant for all x between a and b, and 0 otherwise. Asymptotically approaches the x axis when x increases to + infinity or decreases to -infinity. the cumulative distribution function F(x) of a continuous random variable X with the probability density function f(x) is which of the following? the area under f over all values x. the area under f over all values that are x or less. the area under f over all values that are x or more. the area under f over all non-negative values that are x or less. the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is __. 1/(b - a) between a and b, and zero otherwise. (b - a)/2 between a and b, and zero otherwise (a + b)/2 between a and b, and zero otherwise 1/(a + b) between a and b, and zero otherwise. We are often interested in finding the probability that a continuous random variable assumes a particular value. True False

Explanation / Answer

1. The answer is A. it provides all the probabilities between a and b

2. The answer is B. F(x) gives the area for values less than x

3. The height will be defined as 1/(b-a) because the area of the rectangle should be 1 and the width here is (b-a)

4. False. we are interested in the values less than or equal to a variable or values between 2 variables

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