Find the E(X) of the random variable X with the following PDF: ƒx(x) = ²/2 I[0,1] (x) + ½ 1(1,2) (x) + (−½ + ²) [2,3)(x)
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- Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).Find the variance by calculating the first two moments of the random variable X = (- 1 / λ) ln (1-U), where U ~ U (0,1) and λ> 0.
- Let X be a Gaussian random variable (0,1). Let M = ln(5*X) be a derived random variable. What is E[M]?X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2The probability function of the random variable X is defined as f(x)=cx²(1-x)² for 0<x<1, otherwise f(x)= 0. Calculate the constant c , the expected value and the variance.
- 1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.Given is the PDF of random variable X, where c = 1 and fx(x) = x^2 0<=x<=c. Determine the: 1. value of d to make the PDF valid 2. expected value of X 3. variance of XConsider a random variable X with E[X] = 10, and X being positive. Estimate E[ln√X] using Jensen’s inequality.