Problem 7 Let X ~ Poisson(a) and Y ~ Poisson(ß) be two independent random variables. Define a new random variable as Z = X +Y. Find the PMF of Z.
Q: 2. Let X be a random variable. Is it possible that px,x² = 1 for some X? What about PX,x² = -1?
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Q: ssume that X and Y are random variables with the following parameters: = 13, ly 12, оъ 3 4 апd oy 3,…
A: Solution: Given information: μx= 13 μy= 12 σx= 4σy=3and σxy=0.8
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Q: 2. Suppose that X is a random variable with E(X) = 6 and Var(X) = 4. Find the following: a) Е(4X +…
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A: It is an important part of statistics. It is widely used.
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A: Dear students as per guidelines we answer the first question only. Please post other question in a…
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Q: Suppose Joint PMF of two random variables X and Y are given in below table Y = 0 Y = 1 X =0 X= 1 2…
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Q: 2. Define the characteristic function of a random variable and state its properties.
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Q: Suppose the joint PMF of random variables X and Y is P(X = x, Y = y) = …
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Q: probability distribution of two-dimensional random variable (X,Y)
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Q: Find (i) oý,
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Q: 1) If Var(X-Y) = 2, Var(X+ Y) = 4, E(X) = 3 and E(Y) E(XY)? = 1, than what is
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Q: Where does the z=2 come from? Just from X, and Y also being random variables?
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A: We need show that if X and Y are independent random variables, then E(g(X) | X = xo) = g(xo).
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- 4. Suppose we have random variables W and Q, and we know Var(W) = 25, Var(Q) = 10, and Cov(W, Q) = 2. Now, let A = 2W + 4Q. What is Var(A)?Example 10-3. Show that if X', Y’ are the deviations of the random variables X andY from their respective means, then 1 (1) r =1- 2N X'; Y;\ Ox Oy,For independent random variables X and Y, we have var(X -Y) = var(X)-var(Y ). * true False
- The density function of X is given by f(x): and b. (a + bx² = 0 otherwise 0≤x≤1. If E[X]=, find aThe aim of a study is to test the ratio of variances in the weight of two groups of rats being under a certain drugs A ( group 1) and B ( group 2). A random sample of 17 rats was selected from group 1and 11 rats from group 2, Then their weight were recorded. The results are shown in the following table 2 J غير مجاب عليه بعد الدرجة من 0 2.0 sd Median Mean n 3.0 3.5 17 group 1 2.0 2.20 11 group 2 علم هذا السؤال 1.05 1.15 F19,16,0.025 =0.386 F15,12,0.05 =0.404 F16,10,0.025=0.335 F19.16,0.05 =0.451 F15,12,0.1=0.496 F1610,0.05=0.401 F16,19,0.025 =0.371 F1215,0.05 =0.382 F10,16,0.025 =0.286 F16,19,0.05 =0.437 F1215,0.1=0.475 F10,16,0.05=0.354 Construct a 95% confidence interval for the ratio of the variances. [ Write only the final result in the box below ] 直 a3. If X;~N(0,1), i = 1,2,3,4 are independent Normal random variables and Y is given as Y =(X,+X,)' +(X, + X,)' . If aY~x², . find the constant a. 2
- We have a random variable X1 for population 1 with a mean value of 52 and standard deviation of 3. we have a random variable X2 for population 2 with a mean value of 50 and population standard deviation of 4. we obtain a random sample of 625 elements independently for both populations. what is the probability that the difference in the sample averages X1-X2 is at least 2.3?Suppose X, Y, and Z are three independent normal random variables. X has an expected value of 7 and a standard deviation of 2; Y has an expected value of -2 and a standard deviation of 4; Z has an expected value of 5 and a standard deviation of 12. Let T = 3X + 12Y - 2Z Variable X Y Mean(Expected Value) 7 -2 Standard Deviation 2 4 12 Coefficient 3 12 -2 a) What is the expected value of T? b) What is the variance of Z? c) What is the variance of T? d) What is the standard deviation of T? N LO