1 the discrete random variable x has probability

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Reference no: EM13371850

1. The discrete random variable X has probability distribution given by

a. Find the value of a.

b. Write down E(X)

c. Find the variance of X.

2. Consider the random variable Y = X1 - X2 where X1 and X2 are random variables representing the outcomes of rolling two identical six-sided fair dice.

a. Write down the probability mass function for Y

b. Compute P(Y <0), P(Y <3) and P(-1<Y <1)

3. The average score of a math test in a class of 50 is 70 with standard deviation 10. Assuming this class is a valid representation of the population:

a. Test if the population mean is statistically different to 80 at 5% size?

b. Test if the population mean is statistically less than 75 at 1% size?

c. In conducting these tests, have you had to make any assumptions?

4. An athletics coach estimates a simple linear regression predicting the change in performance (in seconds taken to run a race) for 800m runners by the average hours of training undertaken per week during the pre-season.

R² = 0.965623
Adjusted R² = 0.965564
Standard error of residuals = 0.147378
Observations = 582

2282_Find the variance1.png

a. State the estimated equation.
b. Interpret the estimated coefficients. Do they make sense?
c. Comment on the fit of this model.

5. A bag contains 3 red marbles, 2 black marbles, and 4 white marbles. A student selects three (3) marbles at random (without replacement). What is the probability that the student has selected one marble of each colour?

Reference no: EM13371850

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