Suppose that the probabilities are 0.3, 0.4, 0.1, and 0.2, respectively, that 0, 1, 2, or 3 power failures will strike a certain subdivision in any given year. Find the mean and variance of the random variable X representing the number of power failures striking this subdivision. Calculate the mean, μ. The mean is Calculate the variance, o². The variance is. (Round to two decimal places as needed.) (Round to two decimal places as needed.)

2. Let X - tp. Verify the mean and variance formulas. (Hint: Let X = p/2UV-1/2.)

A sample of 100 scores has a mean of 58, a variance of 160, and an estimated standard error of 4. Which of these values is guaranteed to increase if the sample size is decreased to 10? a. none of these is likely to be changed very much by decreasing n.   b. the value of the variance   c. the value of the mean   d. the value of the standard error

The mean height of 15-year-old boys (in cm) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are normally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys will exceed the mean height of the sample of girls by 1 or more is: O 0.9938 0.9878 0.0062 O 0.9972

The mean height of 15-year-old boys (in em) is 175 and the variance is 64. For girls, the mean is 165 and the variance is 64. Assuming that the two populations are nomally distributed. If eight boys and eight girls were sampled, then the probability that the mean height of the sample of boys would be higher than the mean height of the sample of girls 18: O 0 9878 O 0.0062 O 0.9938 0 9972 Let E[X(Y-1)] 10, E[X(Y#1)] 20, V(X) Then E(Y) 8. V(Y) 12 and V(X+Y) 30. O 14/5 12/5 2

Consider the following data: 7 8 P(X = x) 0.2 0.2 0.2 0.2 0.2 %3D Step 2 of 5: Find the variance. Round your answer to one decimal place. 5.

Please answer the question in the photo. Thank you!

Suppose that we have disjoint normal populations A and B with equal population variances. Suppose we plan a sample of size 4 from from population A and a sample of size 9 from population B which we will pool to form the pooled variance. If you know the population variances are both in fact equal to 6, what is the probability that the pooled variance of the two samples will turn out to be less than 8 given your information? .8 .2 .82 .18 NONE OF THE OTHERS