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**.

Please rate the answer. Thank you.

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