The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X . What are the mean and standard deviation of W ?

The mean and standard devaition of W are 6 and 31 respectively.

Step-by-step explanation:

Given that:

W = 7 + 2X

Variance (W) = Variance(7 + 2X)

For a term constant term, the variance is zero.

So;

W = 4 × Var(X)

W = 4 × (SD (X))²

W = 4 × (3)²

W = 4 × 9

W = 36

Thus, Variance (W) = 36

The standard deviation of W =

W =

W = 6

Also;

E(W) = E(7 +2 X)

E(W) = 7 + 2 × E(X)

where;

mean X = 12

E(W) = 7 + 2(12)

E(W) = 31

Thus, the mean and standard devaition of W are 6 and 31 respectively.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12