QM 235 Test 3

Consider the following cumulative distribution function for the discrete random variable x P(X ≤ x) 1 0.30 2 0.44 3 0.72 4 1.00 What is the probability that X is greater than 2?

0.56

On a particular production line, the likelihood that a light bulb is defective is 5%. Ten light bulbs are randomly selected. What is the probability that none of the light bulbs will be defective?

0.5987

For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the probability that three of the customers redeem the coupon?

0.0486

Consider the following discrete probability distribution. x P(X = x) -10 0.35 0 0.10 10 0.15 20 0.40 What is the probability that X is 0?

0.10

Consider the following cumulative distribution function for the discrete random variable. x 1 2 3 4 P(X ≤ x) 0.30 0.44 0.72 1.00 What is the probability that X equals 2?

0.14

Thirty percent of the CFA candidates have a degree in economics. A random sample of three CFA candidates is selected. What is the probability that none of them has a degree in economics?

0.343

Consider the following discrete probability distribution. x -10 01 0 20 P(X = x) 0.35. 0.10 0.15 0.40 What is the probability that X is negative?

0.35

Consider the following cumulative distribution function for the discrete random variable x P(X ≤ x) 1 0.30 2 0.44 3 0.72 4 1.00 What is the probability that X is less than or equal to 2?

0.44

The expected value of a random variable X can be referred to or denoted as

µ E(X) The population mean **(ALL OF THE ABOVE)**

The expected value of a random variable X can be referred to or denoted as ___________.

µ E(X) The population mean **(All of the above)**

Consider the following probability distribution. xi -2 -1 0 1 P(X = xi) 0.2 0.1 0.3 0.4 The expected value is _____.

-0.1

The number of homes sold by a realtor during a month has the following probability distribution: Number Sold Probability 0 0.20 1 0.40 2 0.40 What is the probability that the realtor sells no more than one house during a month? What is the expected number of homes sold by the realtor during a month?

0.60 1.2

It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that none in a random sample of four calculators is defective?

0.6561

The number of homes sold by a realtor during a month has the following probability distribution: Number Sold. Probability 0 0.20 1 0.40 2 0.40 What is the standard deviation of the number of homes sold by the realtor during a month?

0.75

The number of cars sold by a car salesperson during each of the last 25 weeks is the following: Number Sold 0 1 2 Frequency 10 10 5 What is the probability that the salesperson sells no more than one car during a week?

0.80

Consider the following probability distribution. xi P(X = xi) 0 0.1 1 0.2 2 0.4 3 0.3 The expected value is _____. The variance is ____. The standard deviation is _________.

1.9 0.89 0.94

An analyst has constructed the following probability distribution for firm X's predicted return for the upcoming year. Return Probability -5 0.20 0 0.30 5 0.40 10 0.10 The expected value and the variance of this distribution are _____ and _____.

2........21

Which of the following can be represented by a discrete random variable?

The number of obtained spots when rolling a six-sided die

Sixty percent of a firm's employees are men. Suppose four of the firm's employees are randomly selected. a. What is more likely, finding three men and one woman or two men and two women? b. Do you obtain the same answer as in part a if 70% of the firm's employees had been men?

The probabilities of finding three men and one woman, and two men and two women are the same. No, finding three men and one woman is more likely.

What is a characteristic of the mass function of a discrete random variable X?

The sum of probabilities P(X = x) over all possible values x is 1. For every possible value x, the probability P(X = x) is between 0 and 1. Describes all possible values x with the associated probabilities P(X = x). **(ALL OF THE ABOVE)**

Which of the following can be represented by a continuous random variable?

The time of a flight between Chicago and New York

You are considering buying insurance for your new laptop computer, which you have recently bought for $1,500. The insurance premium for three years is $80. Over the three-year period there is an 8% chance that your laptop computer will require work worth $400, a 3% chance that it will require work worth $800, and a 2% chance that it will completely break down with a scrap value of $100. Should you buy the insurance? (Assume risk neutrality.)

Yes

You are considering buying insurance for your new laptop computer, which you have recently bought for $1,600. The insurance premium for three years is $68. Over the three-year period there is an 8% chance that your laptop computer will require work worth $575, a 4% chance that it will require work worth $645, and a 4% chance that it will completely break down with a scrap value of $170. Should you buy the insurance? (Assume risk neutrality.)

Yes

A consumer who is risk averse is best characterized as

a consumer who demands a positive expected gain as compensation for taking risk

We can think of the expected value of a random variable X as

the long-run average of the random variable values generated over infinitely many independent repetitions