Question

Let X be the number of days that Spongebob needs to be in STAT 100's office hour to do his project. Suppose X has the distribution as follows:

X   P(X)
1   0.3
5   0.39
9   You can find it
12   0.27
Find the expected number of days Spongebob needs to be in the office hour E(X).

Express your answer as a decimal or fraction. Your fraction does not need to be reduced. If your answer is in decimal, make sure to include at least 3 digits after the decimal point.

Answer 1

Solution :

The total probability of a probability distribution must be equal to 1.

i.e. P(X = 1) + P(X = 5) + P(X = 9) + P(X = 12) = 1

0.3 + 0.39 + P(X = 9) + 0.27 = 1

P(X = 9) = 1 - (0.3 + 0.39 + 0.27)

P(X = 9) = 1 - 0.96

P(X = 9) = 0.04

The expected value is given as follows :

The expected number of days Spongebob needs to be in the office hour is 5.85.

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