3. Suppose we are shooting a fixed number of free throws. If we are shooting n free throws, let's define 2 so that each outcome is a string of n letters where each letter is either an "s" for success or an "f" for failure. Thus, if n = 5, the outcome ssfff means that we made the first two free throws and missed the last three. Define a random variable N, which gives the number of successes. (For example, N(ssfƒƒ) = 2.) (a) If n = 5, how many outcomes are in the event {N = 2}? Give 3 different outcomes in that event. (b) Let 0 < p < 1. If every outcome in the event {N = 2} has probability p²(1 − p)³, compute P{N = 2}. (c) Let every outcome in the event {N = k} have probability pk (1 − p)n-k for k = 0, 1, 2, 3, 4, 5, Compute the p.m.f. of N; i.e., compute pN (k) = PN = k.
3. Suppose we are shooting a fixed number of free throws. If we are shooting n free throws, let's define 2 so that each outcome is a string of n letters where each letter is either an "s" for success or an "f" for failure. Thus, if n = 5, the outcome ssfff means that we made the first two free throws and missed the last three. Define a random variable N, which gives the number of successes. (For example, N(ssfƒƒ) = 2.) (a) If n = 5, how many outcomes are in the event {N = 2}? Give 3 different outcomes in that event. (b) Let 0 < p < 1. If every outcome in the event {N = 2} has probability p²(1 − p)³, compute P{N = 2}. (c) Let every outcome in the event {N = k} have probability pk (1 − p)n-k for k = 0, 1, 2, 3, 4, 5, Compute the p.m.f. of N; i.e., compute pN (k) = PN = k.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Transcribed Image Text:3. Suppose we are shooting a fixed number of free throws. If we are shooting n
free throws, let's define 2 so that each outcome is a string of n letters where
each letter is either an "s" for success or an "f" for failure. Thus, if n = 5, the
outcome ssfff means that we made the first two free throws and missed the
last three.
Define a random variable N, which gives the number of successes. (For
example, N(ssfƒƒ) = 2.)
(a) If n = 5, how many outcomes are in the event {N = 2}? Give 3 different
outcomes in that event.
(b) Let 0 < p < 1. If every outcome in the event {N = 2} has probability
p²(1 − p)³, compute P{N = 2}.
(c) Let every outcome in the event {N = k} have probability pk (1 − p)n-k
for k = 0, 1, 2, 3, 4, 5, Compute the p.m.f. of N; i.e., compute pN (k) =
PN = k.
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