Answer :
The Expected value of the random variable having the given probability distribution is 2.25 .
In the question ,
given a probability distribution for the random variable "X" ,
we have to calculate the expected value of X ,
the expected value can be calculated using the formula :
Expected Value = Sum of x*p(x) .
Substituting the values from the given probability distribution ,
we get ,
Expected value = (0×1/8) + (1×1/4) + (2×3/16) + (3×1/4) + (4×1/16) + (5×1/8)
= 0 + 1/4 [tex]+[/tex] 6/16 + 3/4 + 4/16 [tex]+[/tex] 5/8
= 0 + 1/4 [tex]+[/tex] 3/8 + 3/4 [tex]+[/tex] 1/4 + 5/8
taking LCM as 8 and simplifying further , we get
= (2+3+6+2+5)/8
= 18/8
= 2.25
Therefore , the expected value is 2.25 .
The given question is incomplete , the complete question is
Find the expected value of a random variable having the following probability distribution :
x : 0 1 2 3 14 5
Probability : 1/8 1/4 3/16 1/4 1/16 1/8
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