1. (-43) - (-38) 2. 8 - 7 - (-4) 3. (-4)

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

Which of these numbers is the greatest

sasho [114]

Answer:

D

Step-by-step explanation:

A= 3,213,213

B= 780,000

C= 6,300,000

D= 11,014,114

5 0

3 years ago

Cassandra can buy a new Wi-Fi router for $50 or rent one from the internet provider for $5 a month. After a year goes by, how mu

Harman [31]

Answer:

She would save $10

Step-by-step explanation:

What would she pay for a year:

5×12=60

New router:

$50

What she saves:

$60-$50=$10

8 0

3 years ago

The average of 21, 18, 16 and x is 20. what is the value of x?

Radda [10]

Answer: 25

Step-by-step explanation:

21 + 18 +16 + X = 20×4

55 + X = 80

X = 80- 55

5 0

3 years ago

Read 2 more answers

Can sum one help me this is my last question

White raven [17]

Answer:

Option B is correct.

the value of discriminant is, -7

Step-by-step explanation:

Given the equation: $x^2 + x +2 = 0$

To find the value of discriminant $b^2-4ac$

A quadratic equation is of the form $ax^2+bx+c = 0$ where a, b and c are coefficient of the equation.

On comparing with given equation we have;

a = 1 , b = 1 and c = 2

then;

Discriminant = $b^2-4ac =(1)^2 -4(1)(2) =1 -8 = -7$

Therefore, the value of discriminant is, -7

5 0

3 years ago

1. (-43) - (-38) 2. 8 - 7 - (-4) 3. (-4) - (-5) + 6