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- Let the probability distribution function (pdf) for a continuous random variable be defined as f(x) = 1 for 0 < x < 1. What is E[X]? 0 0.10 0.25 0.33 0.50 0.67 0.75 1 None of the above.Given the probability density function f(x) = over the interval [2, 7], find the expected value, the mean, 5 the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation: > Next QuestionThe probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)
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- The random variables X and Y have a joint probability density function given by f(x, y) = way, 0 < x < 3 and 1 < y < x, and 0 otherwise.Q1. Suppose X is a continuous random variable. Find an example of a probability density function for X giving expected value E(X) = 1 and variance V (X) = 3 if X has . . . (a.) a uniform distribution. (b.) an exponential distribution. (c.) a normal distribution. In each case, if there is no such probability density function, explain why this is so.1 Given the probability density function f(x) = over the interval [3,6], find the expected value, the mean, 3 the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation: > Next Question