SOLUTION: 25.If the variance of a random variable X is given Var(X)=3. Then Var(2X) is 30.The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probab

Question 465602: 25.If the variance of a random variable X is given Var(X)=3. Then Var(2X) is
30.The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 6.
31.The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 5.
32.If Var(X)=2, find Var(-3X+4).

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
25.If the variance of a random variable X is given Var(X)=3.
Then Var(2X) is 2^2*Var(x) = 4*3 = 12
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30.The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 6.
----
z(6) = (6-0)/40 = 0.15
P(x < 6) = P(z < 0.15) = 0.5596
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31.The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 5.
---
Same procedure as above.
==============================
32.If Var(X)=2,
find Var(-3X+4) = (-3)^2*Var(x) = 9*2 = 18
====================
Cheers,
Stan H.

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