x will be between 1 and 0
between 1-a/2 and a/2 the range is : r = (1-a/2) - (a/2) = 1 - a
the probability of P(x in r) = r / total
total probability is always = 1
P(x in r) = r / total = (1-a) / 1 = 1-a
Let X be a continuous random variable. Prove that: P(21-; < X < xạ) = 1...
Example 46. Let X be a random variable with PDF liſa - 1), 1<a < 3; f(a) = { à(5 – a), 3 < x < 5; otherwise. Find the CDF of X. @ Bee Leng Lee 2020 (DO NOT DISTRIBUTE) Continuous Random Var Example 46 (cont'd). Find P(1.5 < X < 2.5) and P(X > 4).
8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y <1 0, otherwise a. b. c. Find the marginal PDF of X and Y Find the E(X) and Var(X) Find the P(X> Y)
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
3.98 Let X be a continuous random variable with probability density function f(x) defined on = {xl-π/2 < x < π/2). Give an expression for VIsinX)
Question #37 Let X be a continuous random variable with the following density function: p(-x+ /2) for - 0<x<00. Calculate E[X | X > 0). Possible Answers B 1/727 © 12 D/2TR Ⓡ 1.00
Let X be an exponential random variable such that P(X < 27) = P(X > 27). Calculate E[X|X > 23].
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
Let X be an exponential random variable such that P(X<26) = P(X > 26). Calculate E[X|X > 28]. Answer: CHECK
1. Let x, a € R. Prove that if a <a, then -a < x <a.
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.