X and Y be standard normal random variables with correlation p. Compute the joint and marginal distributions of X+Y and X-Y. Are X+Y and X-Y independent?

Suppose the relationship between Y and X is given by: Y = 30 - 25X + error  What is the expected value of Y when X is 10?

Assume, North Origano, is a country with highest domestic violence cases (approximately5 cases per 1000 families). Working with counselors, a researcher developed thefollowing probability distribution for x= the number of new clients for counseling for 2021. x f(x) 10 0.05 20 0.10 30 0.10 40 0.20 50 0.35 60 0.20 i. compute the expexted value and variance of X.

a, b, d,

Prob & Stat 1

Let X and Y be two independent random variables from exponential distribution with mean 3 and 4, respectively. Find P (6Y > X) Note: Please round your answer to 4 decimal places.

In a continuous distribution the   Multiple Choice   PDF shows the area under the curve.   CDF is used to find left-tail probabilities.   CDF is usually the same as the PDF.   PDF is usually higher than the CDF.

There are two independent random variables X and Y. X has mean 4 and standard deviation , and Y also has mean 4 and standard deviation . A random variable W is the difference between X and Y. That is, W = X - Y. Calculate the mean of W.

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According to the National Association of Colleges and Employers, the 2015 average starting salary for new college graduates in health sciences was $51,541. The average starting salary for new college graduates in business was $53,901 (National Association of Colleges and Employers website). Assume that starting salaries are normally distributed and that the standard deviation for starting salaries for new college graduates in health sciences is $11,000. Assume that the standard deviation for starting salaries for new college graduates in business is $15,000. a. What is the probability that a new college graduate in business will earn a starting salary of at least $65,000 (to 4 decimals)? b. What is the probability that a new college graduate in health sciences will earn a starting salary of at least $65,000 (to 4 decimals)? c. What is the probability that a new college graduate in health sciences will earn a starting salary less than $40,000 (to 4 decimals)? d. How much would a new…