Question 4 (12 points)stocks a and b have the following returns in each of the states given below. boomnormal economyrecessionstock a return12%10%-5%stock b return1%-5%15%the probability of the boom is 0.5, the probability of the normal economy is 0.3 and the probability of the recession is 0.2. (a) calculate the variance of the returns of a and the variance of the returns of b(b) what is the covariance between the returns of a and b? (c) what is the standard deviation of a portfolio of a and b with equal amounts invested in both?

the answer is simply just 6n add the two together as they have an n

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

acd, jgvjgbgbgvhgbhjjn

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus