SOLUTION: a random variable X has the following probability distribution. x|1|2|3|4|5| p(x=x)|1/15|a|1/5|b|1/3| if E(x)=11/3 find the values of a and b

Algebra ->  Probability-and-statistics -> SOLUTION: a random variable X has the following probability distribution. x|1|2|3|4|5| p(x=x)|1/15|a|1/5|b|1/3| if E(x)=11/3 find the values of a and b       Log On


   



Question 634051: a random variable X has the following probability distribution.
x|1|2|3|4|5|
p(x=x)|1/15|a|1/5|b|1/3|
if E(x)=11/3 find the values of a and b

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi,
if E(x)=11/3 find the values of a and b
Two unknowns, needs 2 EQs... to find a and b
I. 1%2F15+%2B+a+%2B+1%2F5+%2B+b+%2B+1%2F3+=+1 or a%2Bb+=+6%2F15+=+2%2F5
II. comes from the E(x) = 11%2F3+=+1%2A%281%2F15%29+%2B+2%2Aa+%2B+3%2A%281%2F5%29+%2B+4%2Ab+%2B+5%2A%281%2F3%29 or 2a+%2B+4b+=+4%2F3
a + b = 2/5
2a + 4b = 4/3 |Verify the 2 Eqs and Solve for a and b