The probability mass function of for W is given by , the expected value(e(w)) is and the expressions for is given by
To solve this problem we have to understand pmf or probability mass function and e(W) or expected value.
Probability mass function is defined as the function which given the probability of a discreet random variable.
The weighted average of the possible values of a random variable with weights given by their respective probabilities is known as expected value.
Jon flips a fair coin until a head is witnessed, and independently Anna Flips a fair coin(a different coin than Jon) until a head is witnessed. Let W be the number of flips between Jon and Anna.
Let us now define the random variable
X: Number of flips done by Jon
Y: Number of flips done by Mocus
So, PMF of X
Simmilarly
Now W=min(X,Y)
So,
a) Now let us derive the probability mass function(pmf) for W:
b) Let us calculate the expected value or e(W)
Solving we get
c) The expression for for K=1,2,3,4....
To learn more about probability mass function:
brainly.com/question/14263946
To learn more about expected value:
brainly.com/question/28197299
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