Page (e) Find the mean (or expected value) and variance of X. 4. For each of the

Question

Page (e) Find the mean (or expected value) and variance of X. 4. For each of the following questions, say whether the random process is a binomial proccess or not, and explain your answer. As part of your explanation, you will want to comment on the potential validity of each of the four things that must be true for a process to be a binomial process. (a) One basketball player attempts 10 free throws and the number of succssful attempts is totalled. Fall 2018 Stat 371 (b) Ten different baskethball players each attempt 1I free throw and the total number of sucessful attempts is totalled. SAMSUNG

Explanation / Answer

a) It is a Binomial process.

If the following four assumptions are satisfied then we can say that the process is a binomial process.

1) sample size = n (or number of trials) is fixed. Here n = 10, so this assumption satisfied.

2) Each replication of the process results in one of two possible outcomes (success or failure),

Here we count successful attempts and so 10 - successful attempts will be failures. So there are only

two outcomes and this assumption is satisfied.

3)The probability of success is same that is constant for each replication(or trial). Here proportion of

making a free trial of a same player is same for each through. Thus this assumption also satisfied.

4) The replications(that is trials) are independent,

Note that, the player get success or failure in any trial is not affect the result of any another trials so the

trials are independents. So this assumption also satisfied.

All the four assumptions are satisfied. So it is a binomial process.

b) It is not a binomial process if the probability of making success of free through is different of each

players. Because if the probability of making success of free through is different of each players then

the 3rd assumption of a binomial process violate. So it is binomial process only if the probabilities

of making success of free through is same of each players, otherwise it is not binomial process.

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