Let X be an exponential random variable such that P(X < 27) = P(X > 27)....
Let X be an exponential random variable such that P(X<26) = P(X > 26). Calculate E[X|X > 28]. Answer: CHECK
Let X be a discrete random variable that follows a Poisson distribution with = 5. What is P(X< 4X > 2) ? Round your answer to at least 3 decimal places. Number
3-) Let ocr<1 o w UUUUU is probability destiny function of X random variable. a- ) Find PlOCXCI) b.) Find Pix > 15) UUUUUU ca) Find € (x) and Var(x) d-) Find the distribution function
number? 10 3. Let X be a continuous random variable with a standard normal distribution. a. Verify that P(-2 < X < 2) > 0.75. b. Compute E(지)· 110]
Let X be a continuous random variable. Prove that: P(21-; < X < xạ) = 1 - a.
For a continuous random variable X, P(27 ≤ X ≤ 74) = 0.35 and P(X > 74) = 0.10. Calculate the following probabilities. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.) For a continuous random variable X, P(27 sxs 74) = 0.35 and PIX> 74) = 0.10. Calculate the following probabilities. (Leave no cells blank - be certain to enter "O" wherever required. Round your answers to 2 decimal...
3. Let X be a random variable and denote by Mx(t) its MGF. Prove that, for any t > 0, we have P[X >Mx(t)e
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
3, Let X be a normal random variable with μ (a) If P(Xc)-0.791, what is the value of c? (b) If P(X<c) 0.36, what is the value of c? (c) If P(X>c) 0.40, what is the value of c? 10, and σ=2.
Problem 4. Let X be a random variable with EIXI4 < oo. Define μ1 = EX and Alk-E(X-μ)k, k 2, 3, 4, and then 03 = 쓺 (skewness), a,--2 (kurtosis) 3/2 (1) Show that if P(X- > z) = P(X-円く-r) for every x > 0, then μ3-0, but not the other way around. (2) Compute as and a when X is Binomial with parameter p, exponential with mean1, uniform on [O, 1], standard normal, and double exponential (fx (x)-(1/2)e-M).