A researcher calculated the values and probabilities for arandom variable X as s

Question

A researcher calculated the values and probabilities for arandom variable X as shown below. Unfortunately, he erased the lastvalue and needs to figure out what it wa. If the mean of X was 2.2,then what was the last value? x = 0, 1 , 3, ? P (x) = 0.4, 0.1, 0.2, 0.3 Thanks! A researcher calculated the values and probabilities for arandom variable X as shown below. Unfortunately, he erased the lastvalue and needs to figure out what it wa. If the mean of X was 2.2,then what was the last value? x = 0, 1 , 3, ? P (x) = 0.4, 0.1, 0.2, 0.3 Thanks!

Explanation / Answer

E(X)=2.2= 0*0.4+1*0.1+3*0.2+c*0.3 --> 2.2 = 0.7 + c*0.3 --> 2.2-0.7 = c*0.3 --> 1.5 = c*0.3 --> c= 1.5/0.3 = 5

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