# Guidance with a random variable problem needed

#### Psychic Lobster

##### New Member
Hello. So I have been trying to solve this problem on my statistics course and I'm having a lot of trouble:

"In BME Bioinstrumentation lab, each student is given one transistor
to use during one experiment. The probability a student destroys a
transistor during this experiment is 0.7. Let random variable X equal the
number of destroyed transistors. In a class of five students, determine:
a)E[X]
b)var[X]
c)E[X|X<4]
d)var[X|X<4]"

This would have been a very easy problem for me, if only I had been provided with a data set. So far I managed to obtain the expectation, since in this case it's just E[X]=0.7*5=3.5 . But i got stuck in the second part. I know that var[X]=E[(X-E[X])^2], that is, the average square distance from the random variable to the mean. But if I don't know the values of X, I can't subtract the mean from them. So I'm totally lost at this. I think that if I can solve this part I will be able to do the rest of the problem on my own. Could anyone give me a hint? Thanks

Edit: I have the numerical solutions for the problem which were provided by my teacher, so I know that the results are a)3.5 b)1.05 c)2.584 and d)0.394
Edit2: I figured out that I can make use of the property E[(X-E[X])^2]=E[X^2]-(E[X])^2.
Edit3: So probably a good way of doing this might be actually calculating the probabilities for X=1, X=2 and so on. Am I on the right path?

Last edited:

##### Member
Hello friend, if you pay attention you will see that this is a random variable of a Binomial, then
$$Var[X]=np(1-p)=5*0.7*(1-0.7)=5*0.7*0.3=1.05$$
For items that) and d) you need to know about hope and conditional variance, but it is not too difficult

#### Psychic Lobster

##### New Member
Thank you! I knew I was missing something very stupid and easy and I couldn't figure out what and it was really frustrating. I think I'll be able to do the rest on my own. Thanks again for your help