<em>✨</em> <em>Using factorisation method</em> <em>✨</em>
Hence , option d is the correct answer
2x + x^2 + 2 is the same as x^2 + 2x + 2
Let Zia's age be = x years
Raj is three years older than Zia, so Raj's age = x+3 years
As the sum of the squares of their ages is 369, so
Factoring 2 out we have,
Now solving this equation,
x=-15 and x=12
Neglect the negative value as x cannot be negative
So x=12
Hence, Zia's age is 12 years and
Raj's age is 12+3 = 15 years
The expectation, E(3y +2) and variance, Var(3y+2) of the random variable are 13.4 and 19.44 respectively
<h3>How to determine the expectation and variance of a random variable?</h3>
The expectations or expected value E(y) of a random variable can be thought of as the “average” value of the random variable. It is also called its mean
By definition:
if y = ax + b
then E(y) = aE(x) + b
where a,b = constant
The variance V(y) of a random variable is the measure of spread for the distribution of a random variable that determines the degree to which the values of a random variable differ from the expected value
By definition
if y = ax + b
V(b) = 0
V(y) = V(ax) + V(b)
= a²V(x) + 0
where a,b = constant
Given: E(y)= 3.8 and Var(y)= 2.16
Calculate E( 3y +2) and Var( 3y+ 2)
E(3y +2) = 3E(y) + 2 since E(y) = 3.8
= 3×3.8 + 2
= 11.4+2
= 13.4
Var(3y+2) = 3²Var(y) + 0
= 9×2.16
= 19.44
Therefore, E(3y +2) is 13.4 and Var(3y+2) is 19.44
Learn more about expectations and variance on:
brainly.com/question/15858152
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