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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 8

Lesson 3: Transforming random variables

# Example: Transforming a discrete random variable

Example of transforming a discrete random variable.

## Want to join the conversation?

• Could someone please explain how to read the question? "The table show the probability distribution of X, the number of shots that Anush makes in a set of 2 attempts" what does this sentence suggest. • The game requires you to shoot 2 free throws. X is the random variable which we make equal to the number of free throws she makes. When you take two shots, one of three things can happen. Either you will miss both shots (X=0), make one shot (X=1), or make both shots (X=2). These are the only possible results for X, therefore X is a discrete random variable, because the possible values of the variable are countable. The probability distribution of X just means to show the probability of each value of X occurring. The table shows the probability of each value of X, therefore it shows the probability distribution of X. There is a 16% chance that she makes zero shots, or P(X=0) = .16. There is a 48% chance that she makes one shot, P(X=1) = .48 and there is a 36% probability that she makes two shots P(X=2) = .36. As you can see, these probabilities add up to 1 because these are the only possible values for X.
• I'm not clear why the mean is 10(1.2) - 15 = 3

If we take the outcomes of the scaled distribution and perform the mean calculation with those values we get:

-15(0.16) + -5(0.45) + 5(0.36) = -2.85

What am I not understanding here? • Why are we scaling the standard deviation by 10? Or rather why is the random variable being scaled by 10? • Could someone help me? Thanks

I understand N = 10x - 15.

But I don't understand why x can be replaced by ux (the mean of x) and get the answer.

I have watched this video for at least 10 times! OMG I am so stupid • What bothers me in such questions is the amount of rounding error that occurs. Calculating from scratch, I have a mean of -2.85, while Sal calculated the new mean from the old mean and came up with -3.
Hope this is pointed out in questions in a way that one knows which answer is required.
(1 vote) • I'm a little bit confused in this exercise. At , the probabilities are preserved because they come from X. I understand and it makes sense to me.

However, I don't understand the following:

As I understand, the mean and std are for both the random variable and probability distribution. Then, if we transform the mean and std (by scaling or shifting), then the probability will also be affected. However, in this exercise, the probabilities don't change, why? Maybe, my understanding is wrong.
(1 vote) • Hi, the following question was in one of the quizzes fo this section:
A construction company submitted bids for three contracts. The company estimates that it has a P percent chance of winning any given bid. Let X represent the number of bids the company wins. Here is the probability distribution of X along with summary statistics.
The question was to calculate the net gain based on the number of bids won given that the cost for each bid is 2000 \$.
When I did the transformation I subtracted the cost for the three bids the company submitted (3*2000) but the solution expresses the net gain as the gross gain for any given bid won minus only 2000 (the cost for that bid). Which does not make sense to me. Whatever number of bids the company wins, the cost will always be 6000.
(1 vote) • Would like to know , why would we need ti find the net gain at first if we can just come up with the "equation" N=10X-15 in the first place. If I came up with that eqt in the first place then I can just skip to and just come up with the answers ( as the original mean and SD were given)
(1 vote) • why is the variance of the transformed random variable
not a^2 *var(N)?  