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.*
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
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)
Fx(x) L - - +--- - + -2 -1 1 2 CDF Ex(x) Let X have CDF Fx(2) shown in a) Find P[X > 0.5] and P[X > 1). b) Find E[X].
Suppose that the cdf of random variable X is Skex-3, X <4 11, X >4 Find k. (2 Points) Find the expected value of X. (2 Points)
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).
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
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
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).
A continuous random variable X has cdf F given by: F(x)x3, x e [0,1] (1, x〉1 a) Determine the pdf of X b) Calculate Pi<X <3/4 c) Calculate E X]