P(y) 40! y! (40-y)! (0.9) (0.1) 4⁰-y ▸ y 0,1,...39,40 E(y)
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- I need help with D&E pleaseExercise 4. Let = {a,b,c,d} and define a probability measure on 222 by P(a) = P(c) = 1/6 and P(b) = P(d) = 1/3. Define random variables X and Y by X(a) = X(b) = 2, X(c) = X(d) = −2 Y(a) = Y(d) = -1, Y(b) = Y(c) = 1. (a) List all sets in σ(Y). (b) Let Z = E(XY), determine Z(a) Z(b), Z(c) and Z(d).Suppose X and Y have the joint probability distribution given by the table shown below. Compute Cov(X,Y). -0.750 O-0.125 -0.625 -0.250 -2 y o 2 0 18 1 BIT 8 x 1 1 4 1 2 0
- Help with step by stepW is a random variable with probabilities for w= 0,1 P(W = w) = {2h + k for w= 2 %3D 3k for w= 3,4 7 find the values of h and k. 10 (а) If P(W <2) = (b) Construct a probability distribution table for W. 4.H.W:-Let x be a discreat random variable whose p.m.f If E(x)= 0.5 -1 2 P(x=x) 0.3 a Find the: 1. value a, b? 2. var (3x+3) 0.5 = -a + 2b -a + 2b =1 %3D ash.
- 2. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.Find the mean of the random variable Y with the given probability mass function. 1 4 p(y) .4 .2 .2 .1 .1 O 2.3 O 3 O 4.6 O 1.8 2]A motorcycle drives from Moraytato Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by x y 0 1 2 3 4 0 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (g) Give the standard deviation of X. Answer=
- Time left 1:2 In one sectlon of STAT 1811 course, there are 10 glrls and 20 boys. What Is the probability that in a randomly selected sample of two students from that section both will be glrls? O a. 0.3333 Ob. 0,1034 O c. 0.1111 d. 0.5000Please solve carefully and thoroughlyX, Y and Z are independent geometric random variables with parameters p1, p2 and p3.a. Find the expected value of the minimum of the three random variables.b. Find the expected value of the second smallest of the three random variables
