[2] [3] (5) (a) A soccer squad contains 3 goalkeepers, 7 defenders, 9 midfielders and 4...
Men's Soccer team has 26 players, which include 7 defenders, 9 midfielders, 7 forwards, and 3 goalkeepers. How many possible ways to select 11 players for the starting lineup, if the team decides to use the 4-4-2 formation (i.e. 4 defenders, 4 midfielder 2 forwards, and 1 goalkeeper)?
Men's Soccer team has 26 players, which include 7 defenders, 9 midfielders, 7 forwards, and 3 goalkeepers. How many possible ways to select 11 players for the starting lineup, if the team decides to use the 4-4-2 formation (i.e., 4 defenders, 4 midfielders, 2 forwards, and 1 goalkeeper)?
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7. (a) Find the number of arrangement of the letters in the word DIFFERENTIAL 2 marks] (i) In one selection session, how many ways to choose 11 football players from 2 marks] (b) 20 players? (ii) How many ways to choose one player for goalkeeper, four defenders, four midfielders and two attackers from the 11 players chosen? 2 marks] (iii) How many ways to arrange five players in the first row and the goalkeeper...
(a) (2 pts) An urn contains 3 red and 5 green balls. At each step of this game, we pick one ball at random, note its color and return the ball to the urn together with anoter ball of the same color. Prove by induction that the probability that the ball we pick a red ball at the n-th step is 3/8. (b) (2pts) Consider any two random variables X, Y of any distirbution and not necesarily independent. Given that...
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
Problem 4 Let X and y be independent Poisson(A) and Poisson(A2) random variables, respectively. i. Write an expression for the PMF of Z -X + Y. i.e.. pz[n] for all possible n. ii. Write an expression for the conditional PMF of X given that Z-n, i.e.. pxjz[kn for all possible k. Which random variable has the same PMF, i.e., is this PMF that of a Bernoulli, binomial, Poisson, geometric, or uniform random variable (which assumes all possible values with equal...
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)...
Problem 5 Let X and Y be random variables with joint PDF Px.y. Let ZX2Y2 and tan-1 (Y/X). Θ i. Find the joint PDF of Z and Θ in terms of the joint PDF of X and Y ii. Find the joint PDF of Z and Θ if X and Y are independent standard normal random variables. What kind of random variables are Z and Θ? Are they independent?
Problem 5 Let X and Y be random variables with joint...
(a) 0.5 pt - Write two ways to compute the variance of X using the expectation operator (b) 0.5 pt -What is Gy(2) called, and how is it computed using the expectation operator? (c) 0.5 pt - Suppose Gx()0.25+0.2522+0.525. Find the mean and variance of X (d) 0.5 pt Write the formulas for the 4th moment and the 4th central moment of Y. (e) 0.5 pt-Which moments of X are equal to lim,→¡警(z) and lim,-(鲁(z) +警(z))? (f) 0.5 pt -...
5. (4 x 5) Suppose that an experiment consists of picking at random a binary string of length five. Consider the following events OEi: the binary string chosen begins with 1; E2: the binary string chosen ends with 1 Es: the binary string chosen has exactly three 1s. Please answer the following questions. a. Find p(E Es) c. Find p(E3 E1 E2) d. Determine whether Ei and e. Determine whether E2 and Es are independent. Ez are independent.