Solve all please .

Given that the probability of a student taking a statistics class is 0.83, and the probability of a student taking a calculus class and a statistics class is 0.66, what is the probability of a student taking a calculus class given that the student takes a statistics class?

Round your answer to three decimal places.

Let X = [X1 X2 denote a bivariate normal (Gaussian ) ran- dom vector. Assume EX = 0 and EXXT Define Y1 = X1 + X2 and Y2 = -X1 + X2 1. Find the joint distribution of Y1 and Y2; find the marginal distributions of Y1 and Y2. 2. Find the conditional density of X1, given Y1; find the conditional den- sity of X1, given Y2. 3. Find the conditional mean and variance of X1, given Y1; find the conditional mean and variance of X1, given Y2.Question 17 (3 points) Which statement BEST describes the difference between Probability and Statistics? . Although probability and statistics are related, probability deals solely with chance and statistics deals solely with randomness. The difference between probability and statistics is slight and they can often be used interchangeably without too much confusion. Although probability and statistics are related, probability deals with the chance of selecting a specific "value" or range of "values" from a known population while statistics describes the make-up of a population from a random sample.Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and length measurements. The results of 100 parts are summarized as follows: Length excellent good Surface excellent 80 2 Finish good 10 Let A denote the event that a randomly selected part has excellent surface finish, and let B denote the event that a randomly selected part has excellent length. Determine: a. P(A) and P(B). b. If the selected part has excellent surface finish, what is the probability that the length is excellent? c. If the selected part has good length, what is the probability that the surface finish is excellent