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Let random variable X be distributed according to the p.m.f P(a) 0.3 0.5 0.2 · If...
Let random variable X be distributed according to the p.m.f P( 0.3 0.5 0.2 · If Y=2X, what are li E r Var(Y) . If Z = aX + b has EZj-0 and Var(Z)-1, what are: lal
1. Two independent random variables X and y are given with their distribution laws 4 P 07 0.1 0.2 P 0.2 0.3 0.5 Find 1) the variance of random variable Y 2) the distribution law of random variable Z-0.5Y+x END TEST IN PROBABL ITY THEORY AND STAISTICS Variant 1 1. Two independent random vanables X and Y are given with their distribution laws: 2 0.7 0.1 P 0.2 0.3 0.5 0.2 Find 1) the variance of random varñable Y 2)...
Let X be a discrete random variable with the following pmf 0.1 for I = 0.2 0.2 for x = 0.4 0.2 for x = 0.5 P(X = x) = 0.3 for x = 0.8 0.2 for x = 1 0 otherwise Note: Write your final answers as decimals Find the following a) P(0.25 < X < 0.75) = b) P(X = 0.2|X<0.6) c) E(2X+1) =
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)
The random variable X has probability distribution 1 3 5 7 9 P(X=x) 0.2 0.3 0.2 0.15 0.15 Find E(X) and Var(X)
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
Let X be a random variable satisfying P(-1 X 1) = 0.3, P(X = 1.5) = 0.1, P(1.5 X P(3 X 7.4) 0.3, P(X 10)0.2 2) = 0.2 Find (i) P(X 2 1.3) (ii) P(X 2.3) ii P(1.5< X 2) (iv) P(1.5 3X 38)
7. Let X be a random variable with the following distribution: -2 3 f(x) 0.3 0.2 a. Find the variance of X. b. Find the standard deviation of X. 5 0.5
X is a random variable uniformly distributed on [-3,1]. 1. Let Y = 2X – 1, find the pdf of Y. 2. Let Z = [X], find the pdf of Z. 3. What is the pdf of Y = [X + 3/?
3. Let X be a discrete random variable with the following PMF: 0.1 for x 0.2 for 0.2 for x=3 Pg(x)=〈 0.1 for x=4 0.25 for x=5 0.15 for x=6 otherwise a) (10 points) Find E[X] b) (10 points) Find Var(X) c) Let Y-* I. (15 points) Find E[Y] II. (15 points) Find Var(Y) X-HX 4. Consider a discrete random variable X with E [X]-4x and Var(X) = σ. Let Y a. (10 points) Find E[Y] b. (20 points) Find...