1. En una tienda de ropa se pusieron en oferta guantes y chamarras. El primer dia se vendieron 6 pares
2 answers:
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P(r/w) is the probability of picking a red rose at first picking and a white rose at second picking.
P(w/r) is the probability of picking a white rose at first picking and a red rose at second picking.
P(r/w) =
×
= 
P(w/r) =
×
=
Notice that the second fraction is out of 18 because the second picking of rose will be out of 18 since the first rose is not replaced.
P(r/w) equals to P(w/r)
P(w/r) is the probability of picking a white rose at first picking and a red rose at second picking.
P(r/w) =
P(w/r) =
Notice that the second fraction is out of 18 because the second picking of rose will be out of 18 since the first rose is not replaced.
P(r/w) equals to P(w/r)
Answer:
(a)
(b)
Step-by-step explanation:
Let X and Y be discrete random variables and E(X) and Var(X) are the Expected Values and Variance of X respectively.
(a)We want to show that E[X + Y ] = E[X] + E[Y ].
When we have two random variables instead of one, we consider their joint distribution function.
For a function f(X,Y) of discrete variables X and Y, we can define
Since f(X,Y)=X+Y
Let us look at the first of these sums.
Similarly,
Combining these two gives the formula:
Therefore:
(b)We want to show that if X and Y are independent random variables, then:
By definition of Variance, we have that:
Since X and Y are independent, Cov(X,Y)=0
Therefore as required: