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Chapter 7: Q14RE (page 495)

Question:

(a) What is the variance of the sum of \(n\) independent random variables?

(b) What is the variance of the number of successes when \(n\) independent Bernoulli trials, each with probability \(p\) of success, are carried out?

Short Answer

Expert verified

Answer

(a) It's equal to the sum of the variances since the trials are independent is the resultant answer.

(b) The variance of the number of successes is given by

\(np(1 - p)\).

Step by step solution

01

Given data 

The given data is probability \(p\).

02

Concept of Probability 

Finding the probability of an event occurring can be thought of as probability

03

Simplify the expression

(a)

It's equal to the sum of the variances since the trials are independent is the resultant answer.

04

Simplify the expression

(b)

The variance of the number of successes is given by \(np(1 - p)\) by adding the answer of Question 12 \(n\) times due to the linearity of variance in independent variables.

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Most popular questions from this chapter

Question:In roulette, a wheel with 38 numbers is spun. Of these, 18 are red, and 18 are black. The other two numbers, which are neither black nor red, are 0 and 00. The probability that when the wheel is spun it lands on any particular

number is 1/38.

(a) What is the probability that the wheel lands on a red number.

(b) What is the probability that the wheel lands on a black number twice in a row.

(c) What is the probability that wheel the lands on 0 or 00.

(d) What is the probability that in five spins the wheel never lands on either 0 or 00.

(e) What is the probability that the wheel lands on one of the first six integers on one spin, but does not land on any of them on the next spin.

Question: Would we reject a message as spam in Example 4

a) using just the fact that the word “undervalued” occurs in the message?

b) using just the fact that the word “stock” occurs in the message?

Question: What is the probability that the sum of the numbers on two dice is even when they are rolled?

Question: A group of six people play the game of “odd person out” to determine who will buy refreshments. Each person flips a fair coin. If there is a person whose outcome is not the same as that of any other member of the group, this person has to buy the refreshments. What is the Probability that there is an odd person out after the coins are flipped once?

Question:

(a) To determine the probability that the player wins the jackpot.

(b)To determine the probability that the player wins 1000000\(, the prize for matching the first five numbers, but not the sixth number drawn.

(c)To determine the probability that a player win 500\), the prize for matching exactly four of the first five numbers, but not the sixth number drawn.

(d) To determine the probability that a player wins 10$, the prize for matching exactly three of the first five numbers but not the sixth number drawn, or for matching exactly two of the first five numbers and the sixth number drawn.
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