Find the coordinates of the centroid. A(-7,-4) B( -3, 5) C (1, -4)

Find the mean, variance &a standard deviation of the binomial distribution with the given values of n and p.

MrMuchimi

A random variable following a binomial distribution over $n$ trials with success probability $p$ has PMF

$f_X(x)=\dbinom nxp^x(1-p)^{n-x}$

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

$\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1$

The mean is given by the expected value of the distribution,

$\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}$
$\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}$

The remaining sum has a summand which is the PMF of yet another binomial distribution with $n-1$ trials and the same success probability, so the sum is 1 and you're left with

$\mathbb E(x)=np=126\times0.27=34.02$

You can similarly derive the variance by computing $\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2$ , but I'll leave that as an exercise for you. You would find that $\mathbb V(X)=np(1-p)$ , so the variance here would be

$\mathbb V(X)=125\times0.27\times0.73=24.8346$

The standard deviation is just the square root of the variance, which is

$\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834$

7 0

3 years ago

a 24 ft ladder is leaning against a 20 ft building, what is the distance between the bottom of the ladder and the base of the bu

madreJ [45]

The distance at the base is 4 feet. Hope this helps.

4 0

2 years ago

When h is one-half and j is one-third, g is 4. if g varies jointly with h and j, what is the value of g when h is 2 and j is 3?

Softa [21]

I don’t know the answer to this question

3 0

2 years ago

Read 2 more answers

You are analyzing the survey results tabulated below. The first survey question (yes/no) is whether the respondent is over 40, a

kolbaska11 [484]

Answer:

Step-by-step explanation:

tryin to cheat in workkeys

5 0

3 years ago

Helllppp porfavor:,)

tatuchka [14]

Answer:

1. x = 67.5

2. x = 2.5

3. x = 35.2

4. x = 2.0

5. x = 17.0

Step-by-step explanation:

Question 1

The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:

2x/9 = 15

2x = 9(15)

Next solve for x:

2x = 135

x = 67.5

Question 2

The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:

20x/8.7 = 5.8

20x = 8.7(5.8)

Next, solve for x:

20x = 50.46

x = 2.523

Round to the nearest tenth:

x = 2.5

Question 3

The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:

5x/16 = 11

5x = 11(16)

Next, solve for x:

5x = 176

x = 35.2

Question 4

The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:

0.5x/0.06 = 17

0.5x = 17(0.06)

Next, solve for x:

0.5x = 1.02

x = 2.04

Round to the nearest tenth:

x = 2.0

Question 5

The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:

29(44)/x = 75

29(44) = 75x

Next, solve for x:

1276 = 75x

x = 17.0133

Round to the nearest tenth:

x = 17.0

7 0

2 years ago