Suppose that X follows a discrete random variable with the following pmf table.
x | 3 | 4 | 5 |
p(x) | 0.3 | 0.4 | 0.3 |
Find the standard deviation of X. Use two decimal points.
Suppose that X follows a discrete random variable with the following pmf table. x 3 4...
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) =
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...
1. Consider a discrete bivariate random variable (X,Y) with the joint pmf given by the table: Y X 1 2 4 1 0 0.1 0.05 2 0.2 0.05 0 4 0.1 0 0.05 8 0.3 0.15 0 Table 0.1: p(, y) a) Find marginal distributions of X and Y, p(x) and pay respectively. b) Find the covariance and the correlation between X and Y.
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
0.25 x-1 0.15 x2 6. Let X be a discrete random variable with PMF: Px(x) 0.2 x-3 0.1 x 4 0.3 x-5 0 otherwise a. (10 points) Find E[X] b. (5 points) Find Var(X)
Let X be a discrete random variable with PMF: a. Find the value of the constant K b. Find P(1 < X ≤ 3)
Let X be a discrete random variable with PMF(a) Find P(X ≤ 9). (b) Find E[X] and Var(X). (c) Find MX(t), where t < ln 3.
4. Suppose X has a discrete uniform distribution: the distribution function of X 5. A random variable Z has the pmf bclow. P (X-х,)-1 , is|2 n. Find 0 Pz(z) 0.20 0.16 0.4 a (1) What is thevalue of a ? (2) What is P(l S Z <3)? (3) What is Fz (1.7)? 6.
he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be numerical values in the range of X. dCDEFGT-Let- What should be in the blank space? F(0) Fx1)