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Statistics help

Can someone help with this question on statistics please:

"The continuous random variable Y has the normal distribution N(10,2squared)

Write down the value of:

a) P(Y = 10)

b) P(Y < 10)"

The answer to a) is 0 and the answer to b) is 0.5. I think I understand why the answer to b) is 0.5 - i.e. because 10 is the mean so 50 percent is above the mean and 50 percent is below the mean (is that right?) - but why is the answer to a) 0?

Thank you!
Reply 1
Avatar for fpmaniac
fpmaniac
2
The probability of an exact value occurring (=) will always be 0 in normal distribution, whether is P(Y=4) or P(Y=10) or anything equals it will always be 0.
Reply 2
Avatar for Zacken
Zacken
22
Original post by juicedesuccess
Can someone help with this question on statistics please:

"The continuous random variable Y has the normal distribution N(10,2squared)

Write down the value of:

a) P(Y = 10)

b) P(Y < 10)"

The answer to a) is 0 and the answer to b) is 0.5. I think I understand why the answer to b) is 0.5 - i.e. because 10 is the mean so 50 percent is above the mean and 50 percent is below the mean (is that right?) - but why is the answer to a) 0?

Thank you!


In more generality then the above, the probability that P(X = a) for some continuous random variable is 0 for all a.

That is, the probability of a continuous random variable is the area underneath the curve; so the probability that it is between a and b is the integral between a and b.

But the probability that is is equal to a, is the integral between a and a of the pdf, which is 0.
Original post by fpmaniac
The probability of an exact value occurring (=) will always be 0 in normal distribution, whether is P(Y=4) or P(Y=10) or anything equals it will always be 0.


Thanks so much for this - it's really helped me out
Original post by Zacken
In more generality then the above, the probability that P(X = a) for some continuous random variable is 0 for all a.

That is, the probability of a continuous random variable is the area underneath the curve; so the probability that it is between a and b is the integral between a and b.

But the probability that is is equal to a, is the integral between a and a of the pdf, which is 0.


Thank you so much for taking the time to answer - I actually understand it now!! Thanks again!
Reply 5
Avatar for Zacken
Zacken
22
Original post by juicedesuccess
Thank you so much for taking the time to answer - I actually understand it now!! Thanks again!


No worries! :smile:

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