Answer:
Step-by-step explanation:
Two consecutive integers be x and (x+1)
x + x +1 = 7²
2x + 1 = 49
2x = 49 - 1
2x = 48
x = 48/2
x = 24
The consecutive integers are: 24,25
Looks like a badly encoded/decoded symbol. It's supposed to be a minus sign, so you're asked to find the expectation of 2<em>X </em>² - <em>Y</em>.
If you don't know how <em>X</em> or <em>Y</em> are distributed, but you know E[<em>X</em> ²] and E[<em>Y</em>], then it's as simple as distributing the expectation over the sum:
E[2<em>X </em>² - <em>Y</em>] = 2 E[<em>X </em>²] - E[<em>Y</em>]
Or, if you're given the expectation and variance of <em>X</em>, you have
Var[<em>X</em>] = E[<em>X</em> ²] - E[<em>X</em>]²
→ E[2<em>X </em>² - <em>Y</em>] = 2 (Var[<em>X</em>] + E[<em>X</em>]²) - E[<em>Y</em>]
Otherwise, you may be given the density function, or joint density, in which case you can determine the expectations by computing an integral or sum.
The missing number is the square-root of the constant term on the left-hand-side, which equals sqrt(1/16)=1/sqrt(16)=1/4.
Check:
(x+1/4)^2=x^2+2*(1/4)x+(1/4)^2=x^2+x/2+1/16. ok
Answer: x= 1/4
A) He wanted to create zero pairs on the left side of the equation to get a positive coefficient of x on the right side
