1. There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2. a) Find the mean of this probability distribution. (ie. Find E[X]). Find the variance and standard deviation of this probability distribution. (i.e. Find V[X] and SD[X]) The random variables M and W are defined as follows: M=X+5 and W = (1/2)X+5 Find E[M] and E[W]. Find V[M] and V[W]. Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores
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1. There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.
a) Find the mean of this probability distribution. (i.e. Find E[X] ). Find the variance and standard deviation of this probability distribution. (i.e. Find V[X] and SD[X]) The random variables M and W are defined as follows: M = X+5 and W = (1/2)X+5 Find E[M] and E[W]. Find V[M] and V[W]. Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores
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![1. There are two boxes. In each box there are 4 cards with a different number printed on it.
The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random
from each box. The random variable X represents the difference between the number on
the card from box 1 minus the number on the card from box 2.
a) Find the mean of this probability distribution. (į.e. Find E[X]). Find the variance and
standard deviation of this probability distribution. (i.e. Find V[X] and SD[X])
The random variables M and Ware defined as follows:
M = X+5 and W = (1/2)X+5
Find E[M] and E[W].
Find V[M] and V[W].
Mary and William play a game using the cards in the above boxes. Randomly two cards are
drawn, and Mary records his score using the random variable M and William uses the random
variable W. They repeat this for a large number of times and compare their scores. Comment on
any likely differences or similarities of their scores](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1febf06f-309a-46d7-944a-698afe377c72%2Faf86f968-0cc5-4bf1-bd6e-9829b26f194b%2Fr1w9rmn_processed.png&w=3840&q=75)
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