Question

Suppose x represents a binomial random variable, and compute

P(x) for each of the following cases. Express your answers to 4
decimal places.
a) n=3, x=2, p=0.1
b) n=8, x=6, p=0.2
c) n=7, x=3, p=0.3

Answer 1

To compute the probability P(x) for each case, we can use the binomial probability formula: P(x) = (nCx) * (p^x) * (1-p)^(n-x).

Step-by-step explanation:

To compute the probability P(x) for each case, we can use the binomial probability formula: P(x) = (nCx) * (p^x) * (1-p)^(n-x), where n is the number of trials, x is the number of successes, and p is the probability of success.

a) For n=3, x=2, and p=0.1: P(x) = (3C2) * (0.1^2) * (1-0.1)^(3-2) = 3 * 0.01 * 0.9 = 0.027.

b) For n=8, x=6, and p=0.2: P(x) = (8C6) * (0.2^6) * (1-0.2)^(8-6) = 28 * 0.000064 * 0.64 = 0.0115.

c) For n=7, x=3, and p=0.3: P(x) = (7C3) * (0.3^3) * (1-0.3)^(7-3) = 35 * 0.027 * 0.2401 = 0.2268.