Tay-Sachs disease is a rare fatal genetic disease occurring chiefly in children,especially of Jewish or Slavic extraction. Suppose that we limit ourselves tofamilies which have (a) exactly three children, and (b) which have both parentscarrying the Tay-Sachs disease. For such parents, each child has independentprobability of getting the disease. Let X to be the random variablerepresenting the number of children that will have the discase. Then E(X2) is

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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If a random variable X is defined such that: E[(X - 2)²] = 18 and E[(X+1)²] = 33. Then the values of u and o are: %3D %3D u = 3 and o = V17 u = 6 and o = 3 and o=32 3/5 and o=6
If x is a binomial random variable, compute p(x) for each of the following cases: (a) n = 5, x = 4, p = 0.2 p(x) = (b) n = 4, x = 2, p = 0.3 p(x) = (c) n = 4, x = 0, p = 0.7 p(x) = (d) n = 5, x = 2, p = 0.5 p(x) =
If X and Y are Gaussian random variables then what is E[XY]?
A- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x= −1,1,2,3. Find the value of k. Find the Variance of X. B- Let x denote a discrete random variable which can take the values −2,0, and 5. Given that the expectation of X is 8/100 and P(X=−2)=8/20 , find P(X=5).
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)
3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
If x is a binomial random variable, compute p(x) for each of the following cases: (a) n = 6, x = 2, p = 0.9 p(x) = (b) n = 6, x = 1, p = 0.3
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
If a random variable X is defined such that E[(X -3)21 = 18 and E(X- 1)1=34, Then the values of u and a are. =3/5 and o=6 and a
X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are given. Find out what the probability P (X = 0) is.

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