TOPIC:Cdf, pdf and expected value.
Suppose that the cdf of random variable X is Skex-3, X <4 11, X >4 Find...
2. A random variable X has a cdf given by F(x) = 1 . x < 0 0 < x < 1 <3 x > 3 11, (f) What is P(X = 1)? (g) Find E(X), the expectation of X. (h) Find the 75th percentile of the distribution. Namely, find the value of 70.75 SO that P(X < 70.75) = F(710.75) = 0.75. (i) Find the conditional probability P(X > X|X > 3).
3. (10 points) Let X be a continuous random variable with CDF for x < -1 Fx(x) = { } (x3 +1) for -1<x<1 for x > 1 and let Y = X5 a. (4 points) Find the CDF of Y. b. (3 points) Find the PDF of Y. c. (3 points) Find E[Y]
Use MATLAB to plot the cdf of X in part (a). .13. A random variable X has cdf: for x <0 Ex(x)-11-le-a for x 0. 4 (a) Plot the cdf and identify the type of random variable. (b) Find P[X s 2], PX 0), P[X < 0], P[2< X < 6], P[X > 10
Additional Problem A: The CDF of random variable X is given by: I< -3 -3 < z< -2 Fx(r) = -2 <I< 2 a) Find the possible range of values that the random variable can take. b) Find E(X) = 4x, the expec ted value. c) Find P(X > 1). d) Find P(X > 1|X > -2).
Let X be a random variable with CDF z<0 G()=/2 0 <IS2 z>2 1 Suppose Y = X2 is another random variable, find (a) P(1/2 X 3/2), (b) P(1s X< 2) (c) P(Y X) (d) P(X 2Y). (f) If Z VX, find the CDF of Z. (d) P(X+Y 3/4)
Let X be an exponential random variable such that P(X < 27) = P(X > 27). Calculate E[X|X > 23].
The cdf of the random variable X is given by: x < a x — а b-0 a < x <b ( 1 x > b Let a=32 and b=79. Find the 87th percentile. Select one: a. 4121.00 O b. 32.00 c. 72.89 d. 79.00 e. 85.16
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
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*