Consider a set of 20 independent and identically distributed uniform random variables in the interval (0,1). What is the expected value and variance of the sum, S, of these random variables? Select one: a.E(S)=10, Var(S)=1.66667 b.E(S)=200, Var(S)=16.6667 c.E(S)=100, Var(S)=200 a.E(S)=10, Var(S)=12

emancipezN 2020-12-30 Answered
Consider a set of 20 independent and identically distributed uniform random variables in the interval (0,1). What is the expected value and variance of the sum, S, of these random variables?
Select one:
a.E(S)=10, Var(S)=1.66667
b.E(S)=200, Var(S)=16.6667
c.E(S)=100, Var(S)=200
a.E(S)=10, Var(S)=12
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Expert Answer

Obiajulu
Answered 2020-12-31 Author has 98 answers

Step 1
Uniform distribution:
A continious random variable X is said to follow Uniform distribution if the probability density function of x is,
f(x)=1ba, where a is lower limit and b is the upper limit of x.
The mean of the Uniform distribution is μ=a+b2.
The variance of the Uniform distribution is σ2=(ba)212.
Step 2
In this case, the iid random variables X1,X2,,X20 follows uniform distribution over the interval (0, 1).
Consider a new random variable S=X1+X2++X20.
Here, it is needed to find the mean and variance of S.
Hence, the mean of Y is,
E(S)=E(X1)+E(X2)++E(X20)
20E(X)[as independentandidentically distributed]
=20(0+12)=10
Hence, the variance of S is,
V(S)=V(X1)+V(X2)++V(X20)
=20V(X)[as independentandidentically distributed]
=20((10)212)=1.66667
Thus, the correct option is a.

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Jeffrey Jordon
Answered 2021-11-14 Author has 2064 answers

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