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Irina-Kira [14]
3 years ago
15

X is a random independent variable with mean 20 and standard deviation of 5. Also suppose that y is a random independent variabl

e with mean of 40 and standard deviation 10. Find the variance and standard deviation of the random variable Z = 2 + 10x
Mathematics
1 answer:
klio [65]3 years ago
4 0
The variable equals 4.
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The following are the answer to this question:

Step-by-step explanation:

In the given question the numeric value is missing which is defined in the attached file please fine it.  

Calculating the probability of the distribution for x:

\to f(x) = 0.19\  for \ x=14\\\\\to  f(x) = 0.29 \ for\ x=7\\\\\to f(x) = 0.38\  for \ x=1\\\\\to f(x)=0.14 \ for \ x=0\\

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\bold{ E(X)= x \times f(x)}

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\bold{E(X^2) = x^2 \times f(x)}

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use formula for calculating the Variance:

\to \bold{\text{Variance}= E(X^2) -[E(X)]^2}

                  = 51.83 - (5.07)^2\\\\= 51.83 -  25.70\\\\=26.13

calculating the value of standard deivation:

Standard Deivation (SD) = \sqrt{Variance}

                                          = \sqrt{26.13} \\\\=5.111

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