Question 851026: An urn contains 10 marbles, each of which shows a number. Five marbles show 1,two marbles show 2 and three show 3.
A marble is drawn at random. If x is the number that shows find the followings:
The probability distribution and the cumulative distribution of the random variable x.
p(1≤x≤3),p(x<3) .
Find the mean of the random variable X.
Calculate the variance and standard deviation of the random variable X.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An urn contains 10 marbles, each of which shows a number.
Five marbles show 1,
two marbles show 2
three show 3.
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A marble is drawn at random.
If x is the number that shows find the following:
The probability distribution and the cumulative distribution of the random variable x
P(x = 1) = 1/2
p(x = 2) = 1/5
p(x = 3) = 3/10
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p(1≤x≤3) = (5/10)+(2/10)+(3/10) = 1
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p(x<3) = 1 - (5/10) + (2/10) = 7/10
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Find the mean of the random variable X.
Mean = 1(5/10)+2(2/10)+3(3/10) = (5 + 4 + 9)/10 = 18/10 = 1.8
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variance = 0.7599
std = 0.8718
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Cheers,
Stan H.
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