For the following distribution: a. Is this a valid probability distribution? Exp

Question

For the following distribution: a. Is this a valid probability distribution? Explain. b. What is the expected value? c. What is the variance of the distribution? d. What is the probability that x is at least 2? Let A be the event X is odd. Let B be the event X is less than 3. e. Are A and B mutually exclusive? Are they independent? f. If you know we select an odd number, what is the probability X is less than 3? g. Compute the probability of the union for A and B. h. Compute the probability of the intersection for A and B.

Explanation / Answer

4 a) For a valid distribution P(X) = 1, and P(X = x) should be between 0 and 1.
0.130+0.346+0.346+0.154+0.026 = 1, Therefore the distribution is valid.

b) E(x) = x*P(x) = 0.130*0 + 0.346*1 + 0.346*2 + 0.154*3 + 0.026*4 = 1.604

c) Var(X) = (x - E(x))2*P(x) = (0 - 1.604)2*0.130 + (1 - 1.604)2*0.346 + (2 - 1.604)2*0.346 + (3 - 1.604)2*0.154
+ (4 - 1.604)2*0.026 = 0.9643

d) P(X <=2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.346 + 0.154 + 0.026 = 0.526

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---