In testing a certain kind of missile, target accuracy is measured by the average distance x at which the missile explodes. the distance x is measured in miles and the sampling distribution of x is given by:

x 0 10 50 100
p(x) 1/40 1? 20 1/10 33/40

calculate the variance of this sampling distribution.

options:

a) 27.6
b) 5138.7
c) 761.0
d) 253.7
e) 88.0
f) none of the above

The answer is c) 761.0

Step-by-step explanation:

Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E (x). Hope is the sum of the product of the probability of each event by the value of that event. It is then defined as shown in the image, Where x is the value of the event, P the probability of its occurrence, "i" the period in which said event occurs and N the total number of periods or observations.

 The variance of a random variable provides an idea of the dispersion of the random variable with respect to its hope. It is then defined as shown in the image.

Then you first calculate E [x] and E [], and then be able to calculate the variance.

E[X]=88

So E[X]²=88²=7744

On the other hand

E[x²]=0+5+250+8250

E[x²]=8505

Then the variance will be:

Var[x]=8505-7744

Var[x]=761

$41

Step-by-step explanation: Hope this help