y P(y) 0 0.64 1 0.25 4 0.11 E(y²) .¹ E(2√Y)
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- Let fxr(r, y) be the joint probability function for the random vector (X, Y). Which of the following staterment is INCORRECT? If both X and Y are discrete random variables, then for any set (aj...,an,b} CR. we must have H ÁXY(4, b) 0, we must have E(Y X = a) = E(Y). If X and Y are independent, then for any a, be R. fxx(a,b) > 0 implies both fx(a) > 0 and fy(b) > 0. Previous Save For Later Next42. a. If X is a discrete random variable with probability mass function P(X =x) and a, b are constants, prove that E(aX +b)= aE(X)+b, ii. Var (ax +b)=a³Var(X). i.
- 2. A random variable X has a probability mass function given by: 1 0.2 a. Determine P(x) = 2 b.Find P(X<2) c. Find P(X≥ 3) X P(x) 0 0.1 2 ? 3 0.4Let XE {-1,0, 1} . That is, X is a discrete random variable only takes three values -1, 0, and 1. Suppose the equality for Chebyshev's inequality holds for X and P(X = 0) = 0.3 , find P(X = 1) Let X be a random variable with probability density f(x) = x6 for x > 1 and O else. Use Chebyshev's inequality to bound P(X > 2.5) . Round your answer to 3 decimal places.Many random number generators allow users to specify the range of the random numbers to be produced. Suppose you specify that the random number Y can take any value between 0 and 6. Then the density curve of the outcomes has constant height between 0 and 6 and height O elsewhere.
- Suppose that the distribution function of X is given by: (0, b<0 b Osb<1 1 b F(b) =- D=1, Isb<2 2 11 2sb<3 12 b23 1. Determine its corresponding probability mass function. 3 2. FindFind c to get a probability mass function.1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
