What is the formula for the expected number of successes in a binomial experiment with n trials and probability of success p?

A. Upper E (Upper X )equalsE(X)=StartRoot np (1 minus p )EndRootnp(1−p)
B. Upper E (Upper X )equalsE(X)=p Superscript npn
C. Upper E (Upper X )equals (1 minus p )Superscript nE(X)=(1−p)n(1 minus p )Superscript n(1−p)n
D. Upper E (Upper X )equalsE(X)=np

The probability mass function for the Binomial distribution is given as:  

Where (nCx) means combinatory and it's given by this formula:  

The expected value is given by this formula:

For this reason the best option is:

D. E (X )=np

Step-by-step explanation:

Previous concepts  

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".  

Solution to the problem

Let X the random variable of interest, on this case we now that:  

The probability mass function for the Binomial distribution is given as:  

Where (nCx) means combinatory and it's given by this formula:  

The expected value is given by this formula:

For this reason the best option is:

D. E (X )=np

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl