Test to determine whether or not P(x) is a binomial probability ...

[evelyn o bentley]

Test to determine whether or not P(x) is a binomial probability function.

Question 2

If this experiment is completed with replacement, explain why x is a binomial random variable.

[FergA]

Answer to Question 1

By inspecting the function P(x) we see it satisfies the following binomial properties: n = 4, p = 0.5, q = 0.5 (p + q = 1), the two exponents x and 4-x add up to n = 4, and x can take on any integer value from zero to n = 4; therefore P(x) is a binomial probability function.

Answer to Question 2

x is a binomial random variable because the trials are independent. n = 4, the number of trials; two outcomes, success = ace and failure = not ace; p = P(ace) = 4/52 and q = P(not ace) = 48/52; x = n (aces drawn in 4 trials) and could be any number 0, 1, 2, 3 or 4 . Further, the probability of success (get an ace) remains 4/52 for each trial throughout the experiment, as long as the card drawn on each trial is replaced before the next trial occurs.

[evelyn o bentley]

Gracias!

[aliotak]

Excellent