## Q.11 In a company, out of 20 employees, five are graduates. Three employees are selected at random, what is the probability that all three are graduates?

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# Probability and Statistics

## 6. + 1/2 points Previous Answers DevoreStat9 2.E.042. My Notes + Ask Your Teacher A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster three centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups with X as guard, then lineups with X as forward.] 144 ✓ lineups (b) Now suppose the roster has 4 guards, 5 forwards, 4 centers, and 2 “swing players” (X and Y) who can play either guard or forward. If 5 of the 15 players are randomly selected, what is the probability that they constitute a legitimate starting lineup? (Round your answer to three decimal places.) 3003

## A bag contains 3 green Christmas ornaments and 4 gold ornaments. If you randomly pick two ornaments from the bag at the same time, what is the probability that both ornaments will be gold?

## If a CD player is programmed to play the CD tracks in random order what is the probability that it will play 6 songs from a CD in order from favourite to least favourite?

## 2.9 Suppose Yt = β0 + β1t + Xt, where {Xt} is a zero-mean stationary series with autocovariance function γk and β0 and β1 are constants.a. Show that {Yt} is not stationary but that Wt = Yt = Yt – Yt-1 is stationary.

## Suppose Y_{t} = 5 + 2t + X_{t} where {X_{t}} is a zero-mean stationary series with autocovariance function

## Yt = 5 − 2t + Xt, where {Xt} is stationary with mean 0 and autocovariance function γk. Now, let Wt = Yt − Yt− (a) Find the mean function for {Wt}. (b) Find the autocovariance function for {Wt}.(c) Is {Wt} stationary? Why or why not?

A starting lineup in basketball consists of two guards, two forwards, and a center. (a) A certain college team has on its roster three centers, four guards, three forwards, and one individual (X) who can play either guard or forward. How many different starting lineups can be created? [Hint: Consider lineups without X, then lineups …

A bag contains 3 green Christmas ornaments and 4 gold ornaments. If you randomly pick two ornaments from the bag at the same time, what is the probability that both ornaments will be gold? EXPERT ANSWER

If a CD player is programmed to play the CD tracks in random order what is the probability that it will play 6 songs from a CD in order from favourite to least favourite? EXPERT ANSWER Total number of possible ways to shuffle 6 songs = 6! = 720 There is only one possible way …

2.9 Suppose Yt = β0 + β1t + Xt, where {Xt} is a zero-mean stationary series with autocovariance function γk and β0 and β1 are constants. a. Show that {Yt} is not stationary but that Wt = Yt = Yt – Yt-1 is stationary. EXPERT ANSWER

Suppose Yt = 5 + 2t + Xt where {Xt} is a zero-mean stationary series with autocovariance function k a.) Find the mean function for {Yt} b.) Find the autocovariance function for {Yt} c.) Is {Yt} stationary? Why or why not? EXPERT ANSWER

Yt = 5 − 2t + Xt, where {Xt} is stationary with mean 0 and autocovariance function γk. Now, let Wt = Yt − Yt− .(a) Find the mean function for {Wt}.(b) Find the autocovariance function for {Wt}.(c) Is {Wt} stationary? Why or why not? EXPERT ANSWER