Problem #9: Suppose that a random variable X has the following probability density function. (c(81-x²) 0≤x≤ 9 0 otherwise f(x) = Find the expected value of X. (You will need to find the value of the constant C so that f is a pdf.)
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- (2.d) We are interested in the function of X defined by Y = g(X) = X². What is CDF of Y in terms of CDF of X? (Note, in %3D the answer box SQRT=Square Root). Referring to Y = g(X) = XWhat is the expected value (2.e) of the function of the random variable, E[Y?can you please expand and explainn this problemQuestion 2: Suppose we have a random sample X₁, X2,..., X, from the following probability density function: f(x;0) 1 - e 20 -1/(20), x>0, 0>0 Derive the maximum likelihood estimator of 0. Be sure to check the second derivative.
- Roll two dice and observe the numbers coming up. Define two events by: A="the sum is six," and B-"the numbers are not equal." Find and compare P(B) and P(BIA).The following table shows the price per share of Apple stock at the beginning of different months. Calculate the four-month weighted moving average for October 2021. Round your answer to the nearest cent. Month July 2021 August 2021 September 2021 October 2021 November 2021 December 2021 Apple Stock Price Simple Moving Average Weighted Moving Average $136.60 $146.36 $152.83 $141.90 $148.99 $167.48 ???Please solve P1
- A technician discovered that the cumulative distribution function (CDF) of the lifespan of bulb in years is given by f(y) = -10 ye 10 100 0[2] X is an exponential random variable with variance 9. If (X, Y = (2, otherwise, 1Rework problem 16 in section 4.2 of your text, involving drawing markers from a box of markers with ink and markers without ink. Assume that the box contains 12 markers: 9 that contain ink and 3 that do not contain ink. A sample of 6 markers is selected and a random variable Y is defined as the number of markers selected which do not have ink. Find the probability density function. Be certain to list the values of Y in ascending order.QUESTION 4 The probability density function for the time taken to complete a 1-hour test (X) by students is given by a) b) c) Find the value of c. f(x) = {cx² + x ! ) 0≤x≤1 elsewhere Find the probability that a randomly selected student will finish in at least half an hour. Calculate the variance of X.solve question 5 a,b,c and dProblem 2 (7 Points) The amount of time in hours that a computer functions before breaking down is a continuous random variable with probability density function: f(x) = }le 100 x 20 Fourth digit of ID What is the probability that? a. A computer will function between 60 and 160 hours before breaking down? (3.5) b. It will function for fewer than 110 hours? (3.5) Third digit of ID Note: Value of A can be calculated based on S f(x)dx = 1.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON