Question

In: Statistics and Probability

If Y1 and Y2 are two independent random variables, each follows the same distribution N(μ,σ), what is the expected value,

If Y₁ and Y₂ are two independent random variables, each follows the same distribution N(μ,σ), what is the expected value,

variance and standard deviation of

a)Y_{1 +} Y₂?

b)Y_{1 -} Y₂?

c)the average,(Y₁+Y₂)/2 ?

Solutions

Expert Solution

Y₁ and Y₂ are two independent random variables, each follows the same distribution N(μ,σ),

This means

The expected value of is

The Variance of is

The expected value of is

The Variance of is

a)Y_{1 +} Y₂?

the expected value is

The variance is

The standard deviation is

ans:

The expected value of is
The variance of is
The standard deviation of is

the expected value is

The variance is

The standard deviation is

ans:

The expected value is 0
The variance is
The standard deviation is

c) the average,(Y₁+Y₂)/2 ?

the expected value is

The variance is

The standard deviation is

ans:

The expected value is
The variance is
The standard deviation is

orchestra answered 1 year ago

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