Which of the following symbols denotes the size/number of the population?

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

Every week Michelle is aid d dollars for working h hours what is the dependant variable in this relationship

svetoff [14.1K]

Answer:

The dependent variable is d

Step-by-step explanation:

Because the dependent variable depends on the independent variable in this case the amount of money she gets is depended on how many hours she work

5 0

4 years ago

4. Combine Like terms: -7(2 + 3x) + (-3x)(-5) + 9* -7x + 5 0 -7X-5 O 7x-5 O 7x + 5

Dima020 [189]

Answer:

-69x-9

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

There are 30 books and there are 5 paragraghs in each chapter.divide 30,5 what does it give you

Tasya [4]

Thirty divided by would be six

3 0

3 years ago

Read 2 more answers

The probability of an event happening is (11/30), what is the probability of the event not happening?

Vladimir [108]

Answer:

19/30

Step-by-step explanation:

The probability of an event happening or a event not happening is 30/30

30/30 - 11/30 = 19/30

There the answer is 19/30

3 0

4 years ago