Question

Gabby likes to start every day by attempting free throws until she makes one. Since she is just starting out, her chances of success on each individual attempt are only 0.10. Let X be the number of attempts she will need in order to get her first made free throw tomorrow. (a) The random variable X is one of the six special types which we studied. Which one? (b) What parameters does this type of random variable have, and what are they in this example? (c) What is the formula for the expectation of this type of random variable in terms of the parameters, in general? (d) What is the expectation of X in this example? (e) What is the formula for the variance of this type of random variable in terms of the parameters, in general? (f) What is the variance of X? (g) What is the standard deviation of X? (h) What is the probability that X is equal to 7? (Write an exact answer. No need to simplify.) (i) Optional: use a computer or calculator to obtain a decimal approximation. (j) What is the probability that X is less than 5? (Write an exact answer. No need to simplify.) (k) Optional: use a computer or calculator to obtain a decimal approximation

Answer 1

(Since there are more than 4 parts i will answer first 4 i.e. a,b,c,d)

(a) The random variable X is one of the six special types which we studied. Which one?

it is a geometric random variable

b) What parameters does this type of random variable have, and what are they in this example?

parameter of geometric random variable is p (probability of success)

here p = 0.10

(c) What is the formula for the expectation of this type of random variable in terms of the parameters, in general?

(d) What is the expectation of X in this example?

E(x) = 1/p

= 1/0.1 = 10

E(x) = 10

P.S. (please upvote if you find the answer satisfactory)