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- The owners manual of your new car states that each front tire should be filled to a pressure of 26psi. Suppose the air pressure in each tire is a random variable, with L-pressure in left front tire and R-pressure in right front tire. Suppose the joint pdf is given by f(1,r) = ( ) P +r); 20 <1< 30; 20Derive the variance of the Student's t distribution using the definition Var (x) = ELX2] - EX)² .It's desired to model the random variable X with a shape that rises to a peak near x=6 and whose possible values are integers 1-6. Copy paste the following lines of code into R: x <- 1:10 shape <- x*(12-x) barplot(shape, names. arg=x) This "shape" isn't a valid PMF because the numbers don't sum to 1. Convert the numbers in "shape" to valid probabilities and report P(X-5). Copy/paste all digits from R into your answer here.Which value for X will result in the greatest relative frequency give discrete random variable X,when X~B(4,1/10)?We have a random variable Y with unknown mean value. We have obtained a random sample of 10 values of the random variable. The values of the sample are given as: Y = 4, 6, 6, 9, 7, 8, 6, 9, 8, 9. Give the estimate of the mean value of Y.The amount of time a student in Justin’s Intro to Statistics course studied for the final exam is uniformly distributed from 0 to 8 hours. What is the probability that a randomly selected student will have studied between 3 and 7 hours for the final?An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood. Assume that x has a distribution that is approximately normal with mean of 7500 and estimated standard deviation of 1750. A test result of x<3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection. What is the probability that on a single test x<3500? Suppose that a doctor uses the average for two tests taken a week apart. What can we say about the probability distribution of ? What is the probability that <3500? Repeat part b with n = 3 tests taken a week apart. Compare your answers for parts a, b, and c. How did the probabilities change as n increased? If a person had <3500 based on three tests, what conclusion would you draw as a doctor or a nurse?Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair dice are cast. Find P ( X = 5 )What is the distribution of X + Y when X and Y are independent random variables with uniform distribution in (0, 1)?Find the probability that the student is female, given that an education degree is not received. P(F|E')SEE MORE QUESTIONS