Let X be Normally Distributed with μ = 80 and σ = 4.5 7) If P(X
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- EX7.8) Let Y be a random variable having a uniform normal distribution such that Y U(2,5) 2 Find the variance of random variable Y.1. Let X be an RV with PDF a. Find the mean of X. b. Find the variance of X. f(x) = {¹ -=| - |x| for x < 1 otherwise1. Let X be an RV with PDF - f(x) = {1 = |x| a. Find the mean of g (X) = 5x² - 1. b. Find the variance of g(x) = 5x² - 1. for x < 1 otherwise
- 4. Let Y U (0, 1). Show that X = -2ln(Y) follows an Exponential distribution with mean 2. pplications8. Given the Beta Distribution where p(x) = B(a,b).ªªa- Calculate the mean and variance B(a, b) = -xª-¹ (1-x)b-1 1 = √₁² 2²- x-¹(1-x)-¹dx = r(a) I (b) I(a + b)*2. Let log Y the median of Y). ~ N (u, o2). Find the distribution of Y and show that P(Y < eH) = 0.5 (i.e., el is
