Probability distributions (CAM)

Identify which of the random variables below is categorical.

• The height of the next student entering a classroom

• The body temperature of a student

• The suburb of where students live

• The number of times a coin is tossed before tails is yeilded.

Why is this table not a valid probability distribution?

• The probabilities do not add up to 1

• There is a negative probability

• There is a probability that is greater than 1

• All of the above

Consider the JBHA actuarial company, which has been successful and yielded profits for the first 2 years of business. With the data in this table, Ridham has made a better prediction on the company's potential profits.

By completing the given table, what are the expected profits of JBHA?

• $350

• $850

• $1350

• $1800

Consider the JBHA actuarial company, which has been successful and yielded profits for the first 2 years of business. With the data in this table, Ridham has made a better prediction on the company's potential profits.

What is the standard deviation of profits generated by the company? (Round to the nearest whole number)

• 3

• 12

• 116

• 496

Ridham is investing in JBHA, which is a new actuarial firm. Every month there is a 65% chance that he will profit $1500 and a 35% chance that he will lose $1000 from these investments. His expected profit after 2 months is:

• −$125

• $125

• $625

• $1250

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• 
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What is the standard deviation and variance of a distribution that takes 1 value?

• Both 0

• Both values will be greater than 0 but the standard deviation is always the square root of variance

• This is a special case where the variance is 0 and the standard deviation is 1

• There is not enough information for us to give a certain response

Given that E(X) = 5 and Var (X) = 3, then E(2X – 1) and Var (2X – 1) equate to:

The sample space of a uniform distribution is {2, 3, 4, 5, 6, 7, 8} . The expected value and variance of this distribution is: