Determine k so that the function below is a joint probability function. 1 f(x, y) = { b 0 y) {k:(2-x)(1-3) 06 2,0 ≤ y ≤1 elsewhere
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Q: Determine the value of k so that the probability function given below can serve as a probability…
A: Explanation of the answer is as follows
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- The time t (in hours) required for a new employee to succesfully learn to operate a machine in a manufacturing process is described by the probability function f(t) = kt/16 – t for 0Solve the below problem. Table 1 contains the probabilities associated with each possible pair of values for Y, and Y, and is known as the joint probability function for Y,and Y2 Table: Probability function for Y, and Y, Yı_ y2 0 1 2 0 1/9 2/9 1/9 2/9 2/9 0 1 | 2 1/9 0 Find F (1, –2) and F(3,3).J and K are independent events. P(J | K) = 0.23. Find P(J)state s probability P(s) realization X(s) realization Y(s) 1 .1 10 20 2 .2 20 30 3 .2 10 10 4 .3 10 30 5 .1 20 10 6 .1 30 20 What is E(Y|X = 20)? a) 65/3 b) 70/3 c) 25 d) 80/3The following function represents joint probability density function for the random variables X and Y. Find the covariance of X and Y. (6xy?,0 < x < 2 0Let X denotes the number of patients who die at a certain hospital in a day. The following table gives the probability function of X. 1 3 4. P(X= x) 0.3 0.25 0.25 0.15 0.05 Find the P(1< X <4) O 0.4 0.95 0.7 O 0.5(Revision.) Let X = Wo.5 + 0.5W1 – 2W2 – W3, where (W1, t > 0) is standard BM. Find the expectation E(X²).Show that each function defined as follows is a probabilitydensity function on the given interval; then find the indicatedprobabilities.Suppose that X and Y have the following joint probability function: f(x, y) 1 4 0.10 0.15 0.20 0.30 0.10 0.15 (a) Find the expected value of g(X, Y) = XY² (b) Find µx and µy. 3 5Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON