6. Suppose X is a random variable with E(X) = 4 and Var(X) = 9. Let Y = 4X + 5. Compute E(Y) and Select one: O a. 25 O b. 16 O c. 21 O d. none
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- Lisa entered a fast food chain to eat, and the chain can serve the food within X minutes after she enters. Suppose further that she eats her food within Y minutes after it is served, independent of the serving time. Let Z = X + Y be the total amount of time that Lisa stays inside the fast food chain. The PDFs of the random variables X and Y are shown below: 0.1 i. ii. fx(x) 10 15 20 x fy (y) 0.1 E fy(y) = 0.1e-0.1y 50 Y What is the probability that Lisa stays within the fast food chain for at most 18 minutes, i.e. P(Z ≤ 18)? What is the expected value (in minutes) that Lisa stays within the fast food chain?Q2 Suppose Y is a discrete random variable such that P(Y = y) = K (1a)-1,0 < a < 1 for y = 1,2,... co. Find the following as an expression of a. a) Value of the unknown K b) The mean and variance of Y.18. Let X be a discrete random variable with V(X) = 3.70, then V(2X) is A. 13.69 B. 5.70 C. 14.80 D. 7.40 epro
- 3. Suppose X1 and X2 are independent random variables with variances o? > 0 and o? > 0, respectively. Let U = X1 and V = X1+ X2. Find p(U, V) in terms of ơ1 and 02.If the variance of X is 0 then the covariance between X and Y O is equal to 1 O is equal to -1 O cannot be determined O is equal to 0 O is equal to the variance of Y. O None of the Above3. Let X and Y be i.i.d. standard normal random variables. Find E[X² +Y°] and E/X² + Y².
- Q2. Let X be a random variable with (a) Find E(X) (b) Find M(t). (0.42 f(x)=0.46 0.12 if x = 0 if x = 1 if x = 214. Let X be a discrete random variable with the following PMF 1 for k = = -2 4 1 for k = -1 Px (k) = for k = 0 8 1 for k = 1 4 1 for k = 2 Define a new random variable Y as y = (x+ 1)² a. Find the range of Y b. Find the PMF of YZV. O *** 0004 : l 36 l ZAIN IQ Asiacell رسالة 1 غير مقروءة Question 1 There are two boxes the first box contains 3 red beads and the second box contains 2 red beads and 3 black beads we select a random bead from the first box and put it on the second box then we take out 2 random beads without replacement. If the random variable x is equal to the number of red beads from the second box A.find the probability function of x B.find p(0: Let X and Y be independent random variables such that with a prob. 1/3 with a prob. 2/3 with a prob. 3/4 with a prob. 1/4 X = 1 = 0 %3D and Y = 2 =- 3 Find (c) E (XY)An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is thh, then N (thh)=2. Suppose that the random variable X is defined in terms of N as follows: X=2N²-6N-4. The values of X are given in the table below. ttt hhh hth hht tht htt thh tth Value of X -4 -4 -8-8-8-8-8-8 Outcome Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X P(X=x) 7 00 X S2. Let X be the mean of a random sample of n = 25 from N(30, 9). Find the probability that the sample mean is between 29.8 and 30.6.SEE MORE QUESTIONS