Hey, I really need some help figuring out this question.

If XX is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

Liula [17]

Answer:

(a) The mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b) The mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c) The mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d) The mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

Step-by-step explanation:

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

The mean, variance and standard deviation of X are:

$\mu=np\\\sigma^{2}=np(1-p)\\\sigma=\sqrt{np(1-p)}$

(a)

For n = 4 and p = 0.40 compute the mean, variance and standard deviation of X as follows:

$\mu=np=4\times0.40=1.60\\\sigma^{2}=np(1-p)=4\times0.40\times(1-0.40)=0.96\\\sigma=\sqrt{np(1-p)}=\sqrt{0.96}=0.98$

Thus, the mean, variance and standard deviation of X are 1.60, 0.96 and 0.98 respectively.

(b)

For n = 4 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

$\mu=np=4\times0.80=3.20\\\sigma^{2}=np(1-p)=4\times0.80\times(1-0.80)=0.64\\\sigma=\sqrt{np(1-p)}=\sqrt{0.64}=0.80$

Thus, the mean, variance and standard deviation of X are 3.20, 0.64 and 0.80 respectively.

(c)

For n = 3 and p = 0.50 compute the mean, variance and standard deviation of X as follows:

$\mu=np=3\times0.50=1.50\\\sigma^{2}=np(1-p)=3\times0.50\times(1-0.50)=0.75\\\sigma=\sqrt{np(1-p)}=\sqrt{0.75}=0.87$

Thus, the mean, variance and standard deviation of X are 1.50, 0.75 and 0.87 respectively.

(d)

For n = 5 and p = 0.80 compute the mean, variance and standard deviation of X as follows:

$\mu=np=5\times0.80=4.00\\\sigma^{2}=np(1-p)=5\times0.80\times(1-0.80)=0.80\\\sigma=\sqrt{np(1-p)}=\sqrt{0.80}=0.89$

Thus, the mean, variance and standard deviation of X are 4.00, 0.80 and 0.89 respectively.

6 0

3 years ago

If f(x) and 1(x) are inverse functions of each other and f(x) = 2x+5, what is ri(8)?

Yakvenalex [24]

Answer:

3/2

Step-by-step explanation:

3 0

4 years ago

A rectangle has a length 3 feet and width 1/4 foot . what is the area of the rectangle?

Olin [163]

When finding the area of a rectangle, you do area=length*width
length= 3
width= 1/4
a= 1/4*3
a=3/4 square feet

8 0

3 years ago

Read 2 more answers

Please help me with this question!

RUDIKE [14]

Answer:

4/10

Step-by-step explanation:

there's 10 equal selections and there's 4 chances that the spinner will land on A. 4/10 = 0.4 on the probability scale

7 0

4 years ago

Write and solve a real world problem in which the part of a whole results in a number greater than the whole itself.

daser333 [38]

I can think of one case like this: when the whole is negative.

for example, if your family has a debt of 200 dollars, this means that the family has -200 dollars.

Now, the family has four members. How much money does each of the member have?

and the way to solve is is this:

-200/4=-50.

so each person "has" -50 dollars, which is more than -200!

5 0

4 years ago