15. A random variable X has the PDF shown in the figure. (N=13) (a) Find the value of the constant K. (b) Write a numerical expression for the CDF $F_X(x)$. (c) Sketch $F_X(x)$, labeling key points (d) Find the probability that X takes a value less than 3. (e) Find the expected value of X.
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Step 1: The sum of the probabilities of all possible values of X must equal 1. Show more…
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Question 1 Find the probability mass function PMF Question 2 If X is a random variable with probability distribution: x -1 0 5 P(x) 0.2 k 0.3 Find the value of k Question 3 The CDF of a random variable X is given by a. Find the value of a? b. Find the PDF of x? c. Find p(x<0.5)?
Madhur L.
1. A random variable X has the PDF given by: f_X(x) = c/2 e^{-(x+2)}, x >= -2 a. Compute the value of the constant C such that f_X(x) is a valid PDF. Then, sketch f_X(x) b. Obtain an expression for the CDF denoted by F_X(x) c. Compute P[X >= 3] d. Compute P[2 <= X < 4] e. Compute P[X < 1 | |X| <= 4]
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'Q4: Let X be a discrete random variable with range Rx = {1,2,3,-} Suppose the PMF of X is given by 1 Px (k) = for k = 1,2,3, 2k a) Find and plot the CDF of X, Fx(c) b) Find P(1 < X < 3).'
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