Discrete Random Variables Prove that fX is a true probability function, find its expected value and variance.             | (x3) (0,8)x (0,2)3-x             if x = 0,1,2,3 fx(x)  = |              | 0                                      in another case

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

Q: Let the function in the figure be a cumulative distribution function for the random variable X. Find…

A: For a finite random variable X, the cumulative distribution function is defined as F(x) = P(X ≤ x).…

Q: If X and Y are independent, then what is the probability of the event Y > 4X?

A: Iy is given that X follows U(0,1), then pdf of X is f(x) = 1, 0 < x < 1 And Y follows U(0,2)…

Q: Let X be a random variable with E(X)= 1 and E[X(X-1)]=4,then evaluate Var(2-3X).

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Q: f (x) x=0,1,2,3 Define the following probability function the value of the expectaion E(X-1) is 1 2…

A:

Q: The random variable X has CDF Fx(x) x 2) d) Determine E(X) e) Determine Var (X)

A: Given, the cdf of random variable  X: F(x) = 0          x< -30.4           -3≤x<5     0.8…

Q: Suppose a random variable has a CDF given by Fx(x) = (1-e-x)u(x). Find the following quantities: (a)…

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

Q: Infant Mortality Infant mortality is an example of a relatively rare event that can be described by…

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Q: Let X and Y be independent, taking on {1,2,3,4,5} with equal probabilities.  E((X+Y)2)=?

A: We have given that X and Y be independent random variables.   The distribution of X is: P( X=x ) =…

Q: A random point (X,Y) is distributed uniformly on the square with vertices (1,1), = on the square.…

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Q: EXERCISE 4. Suppose that X is a continuous random variable whose probability distribution function…

A: a) The value of c is calculated as follows: ∫02c4x-2x2dx=1c4x22-2x3302=1c8-163=1c=38

Q: a) Probability function of X discrete random variable: x = 1,2,3, ....,10 in other cases (CX P(x)…

A: Solution :  The PDF of random variable is given as, P (x) = cx                      x=1,2,3,...,10…

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: a) Find the value of constant a. b) Find P[X < 3]. c) Find the probability that X is odd. d) Find…

A: Solution