1. Below is a plot of the survival function for a random variable X (a) What...
1. Below is a plot of the survival function for a random variable X 2 (a) What properties of this graph guarantee that it is a survival function for a discrete random variable? (b) Find P[x -3) (c) Find P[X > 3) (d) Find P[X <3 (c) l'ind the probability, maz彰fractiou for K
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)
1. The probability mass function of a random variable X is given by Px(n) bv P Yn (a) Find c (Hint: use the relationship that Σο=0 (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3) n-0 n! ex)
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
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
9.) Suppose that X is a continuous random variable with density C(1- if [0,1] px(x) ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function. (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X
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
11. Let X be a continuous random variable with density function fare-102 for 10 f(1) = lo otherwise where a > 0. What is the probability of X greater than or equal to the mode of X?