Question

1.) Although 24% of all Martians have three eyes, only 6% of the members of the...

1.) Although 24% of all Martians have three eyes, only 6% of the members of the Martian Senate are three-eyed.

Which of the following conclusions may be validly drawn from this discrepancy?

This is clear evidence of eyeism. Differences in outcome such as this one prove definitively that Martian society is overrun with eyeists.

While this doesn’t necessarily prove that Mars is overrun by eyeists, it does show that systemic eyeism must be a big problem on the red planet.

This proves that three-eyed Martians must dislike politics.

None of the above.

2.) The expected value of a random variable X…

is the long-run average of X (i.e. if we let X take on N different values, the mean of all these values gets closer and closer to E(X) as N gets larger and larger.)

is the long-run standard deviation of X (i.e. if we let X take on N different values, the standard deviation of all these values gets closer and closer to E(X) as N gets larger and larger.)

is a subjective measure, since different people will expect different things about X.

is the short-run mean of X (i.e. if we let X take on N different values, the mean of all these values gets closer and closer to E(X) as N gets smaller and smaller.)

is the short-run standard deviation of X (i.e. if we let X take on N different values, the standard deviation of all these values gets closer and closer to E(X) as N gets smaller and smaller.)

None of the above.

3.) Suppose that 75% of all people who possess a Washington driver’s license passed the written driver’s license exam on their first try, 20% passed on their second try, 3% on their third try, and 2% on their fourth try. If we let X be the number of times that a randomly chosen Washington driver took the written exam, what is the expected value of X?

1

1.32

1.39

1.46

2

2.12

None of the above

4.) If you roll 7 dice, what’s the probability of rolling exactly 3 sixes?

.002

.016

.065

.078

.234

.429

Homework Answers

Answer #1

1)

Proportion of the members of the Martian Senate who are three-eyed is less than the population proportion of all Martians.

While this doesn’t necessarily prove that Mars is overrun by eyeists, it does show that systemic eyeism must be a big problem on the red planet.

2)

The expected value of a random variable X is,

is the long-run average of X (i.e. if we let X take on N different values, the mean of all these values gets closer and closer to E(X) as N gets larger and larger.)

3)

expected value of X = 1 * 0.75 + 2 * 0.2 + 3 * 0.03 + 4 * 0.02

= 1.32

4)

X ~ Binomial(n = 7, p = 1/6)

= 0.078

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