Question

.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

Use MATLAB to plot the cdf of X in part (a).

Answer 1

Hi.

Matlab command to plot cdf in part a:

fplot(@(x) 1-(1/4)*exp(-2*x),[0,5])

Here I am plotting the function cdf over [0,5]

"Hi. Matlab command to plot cdf in part a: fplot(@(x) 1-(1/4)*exp(-2*x),[0,5]) Here I am plotting the function cdf over [0,5] \r\n Tyree of random variable: - ""continuous"" [As, if is cont., r . v. X is cont.] Also, F is exponential family distribution. P[x lessthanorequalto 2] = 1 - 1/4 e^-4 P[x = 0] = 0 [As distribution is cont.] P[x < 0] = 0 [F(x) = 0 forall x < 0] P[2 < x < 6] = F(6) - F(2) = 1 - 1/4 e^-12 - (1 - 1/4 e^-4) = 1/4(e^-4 - e^-12) P[x > 10] = 1 - P[x lessthanorequalto 10] = 1 - F(10) = 1 - [1 - 1/4 e^-20] = 1/4 e^-20 "

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