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Answer:
(a) The value of <em>k</em> is .
(b) The probability that at most three forms are required is 0.40.
(c) The probability that between two and four forms (inclusive) are required is 0.60.
(d) is not the pmf of <em>y</em>.
Step-by-step explanation:
The random variable <em>Y</em> is defined as the number of forms required of the next applicant.
The probability mass function is defined as:
(a)
The sum of all probabilities of an event is 1.
Use this law to compute the value of <em>k</em>.
Thus, the value of <em>k</em> is .
(b)
Compute the value of P (Y ≤ 3) as follows:
Thus, the probability that at most three forms are required is 0.40.
(c)
Compute the value of P (2 ≤ Y ≤ 4) as follows:
Thus, the probability that between two and four forms (inclusive) are required is 0.60.
(d)
Now, for to be the pmf of Y it has to satisfy the conditions:
<u>Check condition 1:</u>
Condition 1 is fulfilled.
<u>Check condition 2:</u>
Condition 2 is not satisfied.
Thus, is not the pmf of <em>y</em>.