G A sample of 3 items is chosen at random from a box containing 20 items, out of which 4 are defective. Let X be the number of defective items in the sample. Find Var (X), σX, Var (20 − X) and σ20−X.

The variance and standard deviation of X are 0.48 and 0.693 respectively.

The variance and standard deviation of (20 - X) are 0.48 and 0.693 respectively.

Step-by-step explanation:

The variable X is defined as, X = number of defective items in the sample.

In a sample of 20 items there are 4 defective items.

The probability of selecting a defective item is:

A random sample of n = 3 items are selected at random.

The random variable X follows a Binomial distribution with parameters n = 3 and p = 0.20.

The variance of a Binomial distribution is:

Compute the variance of X as follows:

Compute the standard deviation (σ (X)) as follows:

Thus, the variance and standard deviation of X are 0.48 and 0.693 respectively.

Now compute the variance of (20 - X) as follows:

Compute the standard deviation of (20 - X) as follows:

Thus, the variance and standard deviation of (20 - X) are 0.48 and 0.693 respectively.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)