I. Let X be the number of courses that thirty part-time students were taking this term. The probability mass function of X is summarized in the following table. Show your COMPLETE solutions. Number of Courses P(X = x) (x) 1 30 10 30 7 3 30 4 4 30 2 30 2 30 ТОTAL 1. What is P(X < 4)? 2. What is P(2 < X< 6)? 3. Solve for the expected value of a number of courses that part-time students take this term. 2.

T3.1 Thank you.

gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4

The annual rainfall in a certain country varies from 0 to 9 inches and is a random variable with probability density function defined by f(x): - 9.5 x 45 Find the following probabilities for the annual rainfall in a randomly selected year. Round your answers to 4 decimal places as needed. What is the probability that the annual rainfall is greater than 3 inches per year? What is the probability that the annual rainfall is less than 2 inches per year? What is the probability that the annual rainfall is between 2 and 4 inches per year?

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below: X= # of red | 0 | 1 | 2 | 3 | 4 | 5 0.05 | 0.25 | 0.35 | 0.15 | 0.15 | 0.05 P(X=x) a. How many red lights should she expect to hit each day? b. What is the standard deviation?

The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of $204. a. The lambda of this distribution is b. The probability that the cost is larger than $238 is P(x > $238) = c. The probability that the cost is less than $76 is P(x s $76) = d. The probability that the cost is between $185 and $244 is P($185 s x < $244) = e. The 61st percentile is cost of maintenance s

what is the predicted blood pressure for a man aging 25 years?

solve 1.3.6 please and explain the work

In the table below x denotes the X-Tract Company’s projected annual profit (in $1,000).  The table also shows the probability of earning that profit.  The negative value indicates a loss.   x f(x)   x = profit   -100 0.01   f(x) = probability -200 0.04       0         100 0.26       200 0.54       300 0.05       400 0.02         12 If we add $45 to each value in the profit/loss column above, the new variance of profit will be,   a 12,169               b 11,741               c 11,696               d 11,467

Test the following function to determine whether it is a probability function. (Give your answers correct to two decimal places.) P(x) =  x2 + 5 50 , for x = 1, 2, 3, 4 (a) List the probability distribution. P(1) =   P(2) =   P(3) =   P(4) =