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 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 …

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 Read More »

36 36 10. There are 50 competitors in the men’s ski jumping competition. 30 move on to the qualifying round. How many different top 30 finishes can there be (order matters)? A) 501 B) 301 C) 80 D) 1500 E) 1.25 104 11. How many ways can the manager of a baseball team put together a batting order of his nine players, if the shortstop must bat 3rd? A) 40320 B) 504 C) 362880 D) 120960 12. W a CD player is programmed to play the CD tracks in random order and there are six songs on your CD, what is the probability that it will play the songs in order from your favourite to your least favourite? A) 1 B) 2 C) 1 D) 5 E) 1 3 720 360 13. A group of eight grade 11 and five grade 12 students wish to be on the senior prom committee. The committee will consist of three students. What is the probability that only grade 12 students will be elected, assuming that all students have an equal chance of being elected? A) (12 B) C) D) 5 E) 12 F) 8 13 13 13 23 (13 13 6 3 3 3 3

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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?

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 …

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? Read More »

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.

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

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?

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