Question 1

Use the Poisson Table (Appendix A, Table 3) to find P [ X $\ge$ 4] for rate parameter m = 2.4 
A) .779
B) 0.430
C) .221
D) .096

Accepted Answer

To find P(X ≥ 4) for a Poisson distribution with λ = 2.4, we calculate 1 - P(X ≤ 3). Using the Poisson table, P(X ≤ 3) for λ = 2.4 is approximately 0.779. Therefore, P(X ≥ 4) = 1 - 0.779 = 0.221.

Question 2

Consider a Poisson random variable with rate parameter m = 4. Find its:
(a) Mean
(b) Variance
(c) Standard Deviation

Accepted Answer

The answer of Consider a Poisson random variable with rate...

Question 3

Is the Poisson distribution a suitable approximation for to the binomial distribution with n = 55 and p = .03

Accepted Answer

The Poisson distribution is a suitable approximation for the binomial distribution when n is large and p is small, such that np is moderate. Here, np = 55 * 0.03 = 1.65, which is a condition where the Poisson approximation can be used.

Question 4

The probability of red coming up on a roulette wheel that has 18 red, 18 black, and 2 green slots is 18/38 or about .474. If you bet on red a large number of times, what proportion of times will you win. Explain your reasoning.

Accepted Answer

The answer of   The probability of red coming...

Question 5

John and two of his friends have one-on-one basketball tournaments almost every week. Each person plays each other person once. Let X be the number of games that John wins next week X. Based on the results of the games over the past year, John constructs the following probability distribution for X.
  
Find
(a) The expected number of wins.
(b) The standard deviation of the number of wins.
(c) Explain how John should use the results of previous games to construct the tabled probability distribution.

Accepted Answer

The answer of John and two of his friends have...

Question 6

Given the following probability distribution for a random variable X, Find (a) E ( X ) (b) $\sigma$² = Var ( X ) (c) standard deviation of X.

Accepted Answer

The answer of Given the following probability distribution for a...

Question 7

You are traveling to Stockholm, Sweden next month when the average temperature is -1.5 degrees Celsius. Treating this as the expected value of a random variable X, use the properties of expectation to determine the expected value of this temperature, Y , in degrees Fahrenheit. Recall that

Accepted Answer

The answer of You are traveling to Stockholm, Sweden next...

Question 8

About 75% of dog owners buy holiday presents for their dogs. Sup- pose n = 3 dog owners are randomly selected. Use the formula for the binomial distribution to find the probability of:
(a) Two or more buy their dog holiday presents.
(b) At most two buy their dog holiday presents.
(c) Find the expected number of persons, in the sample, who buy their dog holiday presents.

Accepted Answer

The answer of   About 75% of dog owners...

Question 9

The manager of a satellite TV service states that the rate of
interruption of services is .4 per month. Use the Poisson distribution in Table 3 of Appendix A to find
(a) Zero interruptions in one month.
(b) One or more interruptions in one month.
(c) Exact two interruptions in 3 consecutive months.

Accepted Answer

The answer of   The manager of a satellite...

Quiz 5: Probability Distributions

Use the Poisson Table (Appendix A, Table 3) to find P [ X $\ge$ 4] for rate parameter m = 2.4

Consider a Poisson random variable with rate parameter m = 4. Find its: (a) Mean (b) Variance (c) Standard Deviation

Is the Poisson distribution a suitable approximation for to the binomial distribution with n = 55 and p = .03

The probability of red coming up on a roulette wheel that has 18 red, 18 black, and 2 green slots is 18/38 or about .474. If you bet on red a large number of times, what proportion of times will you win. Explain your reasoning.

Given the following probability distribution for a random variable X, $Given the following probability distribution for a random variable X, Find (a) E ( X ) (b) \sigma <sup>2</sup> = Var ( X ) (c) standard deviation of X.$ Find (a) E ( X ) (b) $\sigma$ ² = Var ( X ) (c) standard deviation of X.

You are traveling to Stockholm, Sweden next month when the average temperature is -1.5 degrees Celsius. Treating this as the expected value of a random variable X, use the properties of expectation to determine the expected value of this temperature, Y , in degrees Fahrenheit. Recall that

The manager of a satellite TV service states that the rate of interruption of services is .4 per month. Use the Poisson distribution in Table 3 of Appendix A to find (a) Zero interruptions in one month. (b) One or more interruptions in one month. (c) Exact two interruptions in 3 consecutive months.

Quiz 5: Probability Distributions

Use the Poisson Table (Appendix A, Table 3) to find P [ X ≥\ge≥ 4] for rate parameter m = 2.4

Consider a Poisson random variable with rate parameter m = 4. Find its: (a) Mean (b) Variance (c) Standard Deviation

Is the Poisson distribution a suitable approximation for to the binomial distribution with n = 55 and p = .03

The probability of red coming up on a roulette wheel that has 18 red, 18 black, and 2 green slots is 18/38 or about .474. If you bet on red a large number of times, what proportion of times will you win. Explain your reasoning.

Given the following probability distribution for a random variable X, Find (a) E ( X ) (b) σ\sigmaσ 2 = Var ( X ) (c) standard deviation of X.

You are traveling to Stockholm, Sweden next month when the average temperature is -1.5 degrees Celsius. Treating this as the expected value of a random variable X, use the properties of expectation to determine the expected value of this temperature, Y , in degrees Fahrenheit. Recall that

The manager of a satellite TV service states that the rate of interruption of services is .4 per month. Use the Poisson distribution in Table 3 of Appendix A to find (a) Zero interruptions in one month. (b) One or more interruptions in one month. (c) Exact two interruptions in 3 consecutive months.

Use the Poisson Table (Appendix A, Table 3) to find P [ X $\ge$ 4] for rate parameter m = 2.4

Given the following probability distribution for a random variable X, $Given the following probability distribution for a random variable X, Find (a) E ( X ) (b) \sigma <sup>2</sup> = Var ( X ) (c) standard deviation of X.$ Find (a) E ( X ) (b) $\sigma$ ² = Var ( X ) (c) standard deviation of X.