Just need to verify my answers

1. Mar 19, 2004

tacman

True or false

1. A continuous random variable is the result of a measurement with an instrument of some kind. Answer: FALSE
2. In a discrete probability distribution, the probability of any value of the random variable must be between –1 and + 1. Answer: TRUE
3. The sample space for the experiment of flipping 3 coins is 8. Answer: TRUE
4. Jack and Jill are going to guess whether a card drawn by Pete is a club or not. Pete signals to Jack that the card is black. Therefore Jack has an advantage over Jill in this game. Answer: TRUE
5. If P(A and B) = 0, then A and B are mutually exclusive. Answer: TRUE
6. If P(A and B) = P(A) * P(B), then A and B are independent. Answer: TRUE
7. It takes a big dog to weigh a ton. (I don’t get this question) Answer: FALSE
8. In the standard normal distribution, the area to the left of the mean is –0.5. Answer: FALSE – because it should still be 0.5 not negative.
9. A value of random variable in any probability distribution can never be more than 3 standard deviations from the mean. Answer: TRUE
10. The speed of a car on the freeway is an example of a continuous random variable. Answer: FALSE

thanks to all who help.

2. Mar 19, 2004

matt grime

9 is wrong. 10 might be.

3. Mar 23, 2004

HallsofIvy

1. A continuous random variable is the result of a measurement with an instrument of some kind. Answer: FALSE
Okay, it can be but it doesn't have to be.

2. In a discrete probability distribution, the probability of any value of the random variable must be between –1 and + 1. Answer: TRUE
Oooh! I don't like the way that's written! Of course, such a probability has to be between 0 and 1. That's included in "between -1 and 1" so I would accept it as true but the statement is very misleading!

3. The sample space for the experiment of flipping 3 coins is 8. Answer: TRUE
I have some real issues with this! The sample space contains 8 members (TTT, TTH, etc.) but I would never say the sample space "is 8"! A sample space is not a number.

4. Jack and Jill are going to guess whether a card drawn by Pete is a club or not. Pete signals to Jack that the card is black. Therefore Jack has an advantage over Jill in this game. Answer: TRUE
Well, duuh! (I never did trust those two!)

5. If P(A and B) = 0, then A and B are mutually exclusive. Answer: TRUE
Yes, that's the definition of mutually exclusive.

6. If P(A and B) = P(A) * P(B), then A and B are independent. Answer: TRUE
Again, that's the definition.

7. It takes a big dog to weigh a ton. (I don’t get this question) Answer: FALSE
Completely meaningless. There are no dogs that weigh a ton. Now if it had said "It takes a big man to weigh a ton", I might start thinking about men whose job it is to weigh heavy items but dogs don't do that either!

8. In the standard normal distribution, the area to the left of the mean is –0.5. Answer: FALSE – because it should still be 0.5 not negative.
Of course. Area is never negative. It is the "z" value measuring how far to the left that is negative.

9. A value of random variable in any probability distribution can never be more than 3 standard deviations from the mean. Answer: TRUE
No, of course, not! a random variable in a normal distribution, for example, can take on arbitrarily large positive or negative values. It's just very unlikely.

10. The speed of a car on the freeway is an example of a continuous random variable. Answer: FALSE
One could certainly argue about how accurate you measure and whether it is ever correct to ascribe "continuity" to a physical measurement, but, on the whole, I would say this is TRUE. A cars speed can, theoretically, take on all speeds between 2 given values.