Question

A discrete random variable, X, takes on the values 8, 125, 750, and 3,800, with probabilities...

A discrete random variable, X, takes on the values 8, 125, 750, and 3,800, with probabilities 0.70, 0.15, 0.10, 0.05, respectively. Use the statistical capacity of your calculator to find the standard deviation of the random variable, X, rounded to two decimal places. Note that this is a probability distribution.

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Answer #1

Solution :-

Data ,

x = 8,125,750,3800

p (x) = 0.70,0.15,0.10,0.05

Mean = X * P(X)

= (8* 0.70 ) + ( 125*0.15 ) + ( 750*0.10 ) + (3800*0.05)

= 5.6+ 18.75+ 75 +190

= 289.35

   = 289.35

Standard deviation = = =X 2 * P(X) - 2

(82* 0.70 ) + ( 1252*0.15 ) + ( 7502*0.10 ) + (38002*0.05) - 289.352

= ( 44.8+ 2343.75 + 56250 + 722000 ) - 83723.4225

= (780638.55 - 83723.4225 )

   =696915.1275

= 834.81

standard deviation = 834.81

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