When the expected value and variance are 3.5 and 15.25, the statistic probability distribution will be 5/10, 3/10, and 2/10.
Given that,
A box contains ten sealed envelopes labelled 1, 2, 3, and 10. Six of them are empty, two have $5 apiece, and the remaining two each contain a $10 bill. You obtain the most money in any chosen envelope when replacement is used; a sample of size 3 is selected (forming a random sample). The statistic of interest is m if the quantities in the selected envelopes are represented by x1, x2, and x3.
We know that,
The probability distribution will be
P(X=0) = 5/10
P(X=5) = 3/10
P(X=10) = 2/10
In probability theory, the expected value is a development of the weighted average. The arithmetic mean of a sizable number of outcomes of a random variable that were independently selected is, informally, the expected value.
The expected value is
E =0(5/10)+5(3/10)+10(2/10) = 3.5
The variance is
V = 0² x (5/10) + 5² ( 3/10 ) + 10² x (2/10) - 3.5² = 15.25
Therefore, the statistic probability distribution will be 5/10, 3/10, and 2/10 when the expected value and variance are 3.5 and 15.25.
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