1. Let X represent the number of times your professor goes to the gym 
each week.  You are given the following probability table for X. 
Unfortunately, your professor spilled some coffee on the probability 
for x = 5 and it is now illegible.

x          1      2      3      4     5
P(X = x) 0.12   0.25   0.38   0.17   ???

(a)	What is P(X = 5)?

All the probabilities must add up to 1, the probability of certainty,
because it is certain that one of them will occur.

So add 0.12 + 0.25 + 0.38 + 0.17 and get 0.92
Then subtract 1.00 - 0.92, and get 0.08

So now we know that what he spilled coffee on was 0.08

x          1      2      3      4     5
P(X = x) 0.12   0.25   0.38   0.17  0.08 

(b)	Find the expected value of X.

Multiply each x by the corresponding probability P(X=x) and add:

E(X) = 1×0.12 + 2×0.25 + 3×0.38 + 4×0.17 + 5×0.08 = 2.84 

(c)	Find the standard deviation of X.



E(X) = 2.84

E(X²) = 1²×0.12 + 2²×0.25 + 3²×0.38 + 4²×0.17 + 5²×0.08 = 9.26





Edwin
 

RELATED QUESTIONS

Let X ∼ N(12, 5). Find the value of x0 such that
(a) P(X > x0) = 0.05
(b) P(X < x0) =  (answered by ewatrrr)

Use Table A0 in Appendix I to find the following: 
a) P(x < 12) for n = 20, p = 0.5 
b)  (answered by math_tutor2020)

Suppose P(x) is a polynomial of smallest possible degree such that:
* P(x) has rational... (answered by ikleyn)

A random variable X has a CDF such that
       x/2    0 < x ≤ 1
F(x) = 
       x-1/2  (answered by Edwin McCravy,math_tutor2020)

A random variable X has a cumulative distribution function
F(x) =
8
<
:
1
2x if 0 <  (answered by ikleyn)

X has a normal distribution with a mean of 75.0 and a standard deviation of 3.5. Find the  (answered by stanbon,LloydB)

The probability distribution of the random variable X is shown in the accompanying table.
 (answered by ewatrrr)

4. X is normally distributed with mean 12 and standard deviation 4.
(a) (3 points)Find... (answered by jim_thompson5910)

consider a binomial random variable X with n=5 and p=0.40
a. Find the probability... (answered by Boreal)