E(X) = (-1)(0.4) + 0(0.3) + 2(0.3) = 0.2
E(X2) = (-1)2(0.4) + 02(0.3) + 22(0.3) = 1.6
So,
Var(X) = E(X2) - [E(X)]2 = 1.6 - 0.22 = 1.56
Also,
E(X4) = (-1)4(0.4) + 04(0.3) + 24(0.3) = 5.2
Problem 2. Consider a random variable with P(X10.4, P(X 0)0.3, P(X Find the median, cumulative distribution...
Random variable X has a distribution: P(x=0)=0.2 ; P(x=1)=0.3 ; P(x=2)=0.1 & P(x=3)=0.3 ; P(x=4)=0.1. Find: a) E(x) and Var(x) b) Find Fx(Xo) c) Find quantile of order 1/4 and median d) Find P(2<=x<=4)
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12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a Inz, a<<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function S(x) for X. (d) Find E(X)
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2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.