.1 The highest score in a game of dice(a) A random variable X is defined as the larger of the scores obtained in two throws of anunbiased, six-sided, die. Show that(2x - 1)Pr(Xx) =x = 1, 2, . .., 6.%3D36(b) A random variable Y is defined as the highest score obtained in k independent throws ofan unbiased, six-sided, die. Find an expression for the probability function of Y.

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Answered: .1 The highest score in a game of dice…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A docs.google.com/forms/d/e (1) Let X be a random variable with p.d.f. fx) =- , then O.w (b) k- (0) k = (a) k=1 (d) k-5 (e) None of these a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer (2) Let X be a random variable with a function x= 0,1, 2,3 4 x! (3-x)! f(x) = , then p(x<1) is 0.w (b) (d) (e) None of these 27 (a) 27 (c) 27 a is the correct answer b is the correct answer c is the correct answer d is the correct answer e is the correct answer
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (*) 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 ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X=2N -2. The values of X are given in the table below. Outcome ttt hth tht htt thh hhh hht tth Value of X -2 2 0 0 2 4 2 0 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the valuesof X. Then fill in the appropriate probabilities in the second row. Value x of X ___ ___ ___ ___ P(x=x) ___ ___ ___ ___
2. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.
32 - The random variable X, which shows the grades of the students in a class in the exam of the statistics course, has a normal distribution with a mean of 80 and a variance of 25. Which of the following is the lowest grade with a probability of 0.3015? a) 32.5 B) 55 NS) 82.5 D) 68 TO) 89
A red die is rolled and then a green die. Let X=2(Spots on Red) + (Spots on Green). Determine the pmf for the random variable. In particular f(6)
Three statistically independent random variables X₁, X₂ and X₂ have mean values X₁ =3, X₂ = 6 and X₂ = -2. Find the mean values of the following functions: 1 2 (a) (b) g(X₁, X₂, X3)= X₁ +3X₂ + 4X3 29 g(X₁, X₂, X3) = X₁X₂X₂ 29
(3) Let X be a random variable with p.d.f 2 (3x+6) 15 then E(x) is 11 12 (b) 30 (c) 30 (d) (e) None of these 33 716
(a) In an experiment, a pair of dice (green and blue) are tossed and the numbers that come up are recorded. Assume that the first outcome is for the green die whereas the second outcome is for the blue die. (i) List the sample space S; (ii) List the elements for event X = {sum is greater than 8}; (iii) List the elements for event Y = {2 occurs on either die or both}; (iv) List the elements for event Z= {number greater than 4 comes up on the green die}; (v) List the elements corresponding to the event X Z; (vi) List the elements corresponding to the event Y N Z;
Q. 1 Deal two cards from a well-shuffled deck of cards. Let the random variable X be the number of aces dealt and let the random variable Y be the number of face cards dealt. (i) Find and sketch fx.y (x, y).
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(Y) = 4 Var(X) = 24 Var(Y) 18 Var(z)=7 E(X)= -3 E(Z) =-1 Compute the values of the expressions below. E(-4-5X)= 0 %3D ? ()- 0 Var(-3+2.X) = 0
Consider a random variable x N(6, 4). Then Prob(X = 12) equals: %3D 0.0 O 0.25 O 0.5 O 0.75 O 0.32
Consider a random experiment of throwing three perfectly balanced and identical coins. Suppose that for each toss that comes up heads we win $3, but for each toss that comes up tails we lose $4. Clearly, a quantity of interest in this situation is our total wining. Let X denote this quantity. (a) What are the values that the random variable X takes? (b) Find P(X = 9). (c) Find P(X = -5). (d) Find P(X = 2). (e) Find P(X = -12). (f) Find P(X = 3). (g) Find P(X =-1).

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