The distribution function for a random variable X is F (x) = {6 z 2 0 , z<0 which of the following gives the probability that the random variable -3 < X< 4? O e-8 – 1 01-e-8 01-e-4 O e-4 – 1

Q: Question 1. Let X and Y be independent random variables. Suppose that the moment generating…

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Q: Find the value of, (i) k (ii) P(X < 2) (iii) P(2 <X< 5).

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Q: Determine the value c so that each of the following functions can serve as a probability…

A: a) It is needed to find the value of c.

Q: The cumulative distribution function for a random variable X is given by: (1-e for x20 F(x)={…

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Q: Let X be a random variable. Which of the following statement is INCORRECT? If V (X) > 0, then for…

A: we know that variance is always positive that is V(X)&gt;0 and also probability is in range [0,1],…

Q: discrete random variable X has the following probability distribution: Value of X 1 2 3 4 5 6…

A: Given that  Probability distribution table X 1 2 3 4 5 6 P(X) 0.30 0.20 0.15 0.15 0.10 0.10…

Q: Let X be the random variable, and create two new copies of this X₁, X₂ ~X x | P(X = x) 0 0.5 1 0.2 2…

A: To determine whether 2X and X1 + X2 have the same distribution, we need to compute their respective…

Q: Suppose that X, Y, and 2 are jointly distributed random variables, that is, they are defined on the…

A: Given that E(X)=-8E(Y)=6E(Z)=-1Var(X)=33Var(Y)=25Var(Z)=48

Q: The probability distribution function of a discrete random variable X is x2 55 ,x = 1,2,3,4,5 0,…

A: Find  Var(3X+2)=? 5E(2X-1)=? E(2X+1)2=?

Q: Roll a red die and a green die. Let the random variable be the larger of the two numbers if they are…

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Q: Let Xbe a random variable with probability distribution as shown below: -1sxs2 S(x)={3 and g(X)-4X…

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Q: 1-4x 10) If a random variable assumes 4 values with probability 1+3x 1-x 1+2x and ¹-4 4 4 4 the…

A: Here for given probability check whether using value of x total probability is equal to 1 and all…

Q: L10Q1.The probability distribution of a random variable is given below. X 0 1 2 P(X) 2 a a 3 a Find…

A: X 0 1 2 P(X) 2 a a 3 a

Q: Let X be a random variable with probability distribution as shown below: 25 2 <x< 10 f(x) = and g(X)…

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Q: 1-4x and 4 1+3x 1-x 1+2x (5) If a random variable assumes 4 values with probability the 4 4 4…

A: If the random variable assumes 4 values , then the sum of all probabilities for x should be equal to…

Q: (2) Let X be a random variable with p.d.f. 1<x<10 f(x) = then o.w 3 (a) k=2 (b) k=8 (c) k = (d) k=3…

A: Solution: 2. From the given information, the probability density function of X is

Q: 4 Let X be a discrete random variable with PGF P,(s) = () %3D 3 Find the probability distribution of…

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Q: Let X and Y be normaly distributed random variables. Which of the following are also normally…

A: Here, given that x and y are normally distributed normal variables. Then , we have to check the…

Q: 4

A: The value of mean is given as, Ex=1.5. The value of variance is given as, varx=0.25. To determine…

Q: X be the random Variable with the following probability distribution: X: 3 6 9 Р(X): 1/6 1/2 1/3 (d)…

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Q: (a) g(X1, X2, X3) = X1 + 3X2 + 4X3 (b) g(X1, X, X3) = X1 X2 X3

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Q: Q4. The following table shows the probability mass function for the discrete random variable X: k 2…

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Q: The probability generating function for a random variable X is given by: 1 1 ,10 1 1 ,20 .2 -725…

A: From a given probability generating function, we need to find required probability

Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

A: From the given information, X P(X=x) -2 0.1 1 0.23 4   5 0.13 6   Let P(X=4)=a and…

Q: (7) A random variable X will take one of its possible values (z) as its actual value, its…

A: Given data is xi P(xi) -2 0.1 0 0.2 5 0.2 8 0.3 10 0.2

Q: If X is a continuous random variable that takes on values between 10 and 40, then the P(X = 15.5) =…

A: We have given that  X is a continuous random variable that takes on values between 10 and 40, then…

Q: 2 The cumulative distribution of a discrete random variable is given by - 2 -1 1 1 1 -+a 6. 17 -5a…

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Q: H P(x)-s/4, what ore the possible vakues ot X tor it to be a probability distribution? etta What in…

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Q: Let X be a random variable. Which of the following statement is INCORRECT? If V (X) = 0, then there…

A: In statistics random variable is a variable whose value will be defined on the basis of a random…

Q: None

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Q: The random variable A has range (0, 1), and p.d.I. given by f(x)=3(x-1)², 0<x< 1. (a) Explain why…

A: Solution: The probability density function of random variable X is  f(x)=3(x-1)2        for…

Q: B/ Let Y denotes a random variable having a negative binomial distribution, with p=(2*G/10) . Find…

A: Negative binomial distribution is used to estimate the probability of number of trials required to…

Q: Let Y be a discrete random variable with generating function 4 Gy (s) 6 - s s2 What is E(Y) (in…

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Q: A random variable X has a following probability function, X 01 2 3 4 5 6 7 P(X) 0k 2k | 2k 3k K 2k2…

A: Answer - Given probability distribution  table         X 0 1 2 3 4 5 6 7 P(X) 0 k 2k 2k 3k k2…

Q: Q.6 a) Let X be a random variable with probability distribution -1 1 2 3 f(x) 0.125 0.50 0.20 0.05…

A: Step 1; Mean of x, E(x) = ∑x* f(x) Variance of x, V(x) = E(x2)-(E(x))2

Q: (2) Let X be a random variable with p.d.f. ke sx)={ then O.w

A: We have to use properties of probability function.