Let X be a random variable with pmf P(0)=0.2, P(1)-0.5, P(2)=0.3. Let F(X) be the cdf of X. (a) Find P(X<0.7) (b)Find F(1.3). (c) Find F(3).
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- A fair coin is tossed three times and the random variable x equals the total number of heads. Find the sketch F(x) and f(x).Consider that a pdf of a random variable X is 1 -25x53 fx (x) ={K otherwise and another random variable Y = 2X. Then find (a) value K, (b) E[X], (c) E[Y] and ( d) EΧΥ.Let X be a random variable taking positive values and assume that E(X) exists. Which of the following statements are true? • (i) E(X*) > (E(X))*. • (ii) E(1/X²) > 1/E(X²). • (ii) E(e-3X) > e°
- If the odds against T occurring are 8:5, then find P(T) and P(T'). P(T) = (Simplify your answer.) P(T') = (Simplify your answer.)X is a random variable that has the following PDF function: fx(x) = 0.28(x + 2) + 0.38(x + 1) + 0.358(x) + 0.158(x – 1) %3D For y = x2, find: 1- fy) 2- Fy(y) 3- E[y] 4- o2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. (a) Find P(X1 = 2 and X2 = 2). (b) Find P(X1 + X2 = 1). (c) Find E(X1 + X2). (d) Find Var(X1 + X2).
- Suppose X is a random variable with cdf 0 Love- 1 (a) Find E(X). (b) Find P(X 1Consider the random variable X with PDF (known as Cauchy distri- bution) f(x) = 7 - 00X - exp (1). Determine the function g (X) defined depending on the random variable X. After determining the function g (X) and assigning a value to 1, E [g (X) | {X> 3}] conditional expected Calculate the value,If E[X] = 1 and Var(X) = 5, use definition of variance and properties of expectation to find (a) E[(2 + X)^2] (b) V ar(aX) for any constant a. (c) V ar(X + b) for any constant b. (d) V ar(4 + 3X)Let X be a continuous random variable with p.d.f. f(x) and distribution function F(x). If Y = X², (a) what is the g(y)? 14/12 (b) If ƒ(x) = -√2/² 2π -∞Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON