MATHEMATICS COLLEGE

Question Two :A discrete random variable X has negative binomial distribution,
with 6 successes required each with probability of success 0.4
Determine the value of ...
a) ...E(X).
b) ... Var( X)
c) ... P ( X = 12).

Answers

Answer 1
Answer:

Using the negative binomial distribution, it is found that:

a) E(X) = 15

b) Var(X) = 6.67

c) P(X = 12) = 0.0883

Negative binomial distribution:

It is the number of trials until q successes of a binomial variable, with p probability of success.

The expected value is:

E(X) = (q)/(p)

The variance is:

Var(X) = (pq)/((1 - p)^2)

The probability mass function is:

P(X = x) = C_(x+q-1,q-1)(1 - p)^xp^q

C_(n,x) = (n!)/(x!(n-x)!)

In this problem, the parameters are: q = 6, p = 0.4.

Item a:

E(X) = (6)/(0.4) = 15

Item b:

Var(X) = (6(0.4))/((1 - 0.4)^2) = 6.67

Item c:

P(X = 12) = C_(17,5)(0.6)^12(0.4)^6 = 0.0883

To learn more about the negative binomial distribution, you can take a look at brainly.com/question/15246027

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1. 2x2 + 3xy + 3xy is equivalent to
Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 180° counterclockwise.U′(1, −1), V′(0, 4), W′(4, 1) U′(−1, −1), V′(4, 0), W′(1, 4) U′(−1, 1), V′(4, 0), W′(1, −4) U′(−1, 1), V′(0, −4), W′(−4, −1)
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Help please it’s supposed to be turned in

Answers

Answer:

30 i believe

Step-by-step explanation:

hope this helps. i say 30 because thats the only common multiple in those numbers :P

The product of 3 and a number is the same as 24 less thrice that same number

Answers

Answer:

there is no such number

Step-by-step explanation:

our "number" will be represented by variable x

3x = 3x-24

isolating x

0x = -24

0 = -24

since this statement is false for all x, there is no such number x

Final answer:

The given condition does not have a solution.

Explanation:

In this question, we are asked to find a number that satisfies the given condition. Let's assume the number is 'x'. According to the given information, the product of 3 and the number 'x' is equal to 24 less than 3 times the number 'x'. We can write this as the equation 3x = 3x - 24. By subtracting 3x from both sides, we get 0 = -24. This means that there is no number that satisfies the given condition.

Learn more about Equations here:

brainly.com/question/9585437

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Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page

Answers

Answer:

13 pages : 1/2 hour Multiply both sides by 2

26 pages : 1 hour ------>> 26 pages/hr

Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages

Split up the fraction: (1/26) hr / page

Answer:

26

Step-by-step explanation:

13 in 1/2 hour

13:1/2

26:1

Need help please show how you did it.

Answers

Answer:

(0, 1).

Method 1 (Substitution):

Substituting our two y's, we get the following:

x^2 + 5x + 1 = x^2 + 2x + 1 \Rightarrow 3x = 0 \Rightarrow x = 0

Thus, the only set of solutions is (0, 1). A quick sketch (either by hand or on Desmos) can confirm this.

Method 2 (Elimination):

We have two equations. We'll let the top one be equation 1 and the bottom one be equation 2. Eliminating as many variables as we can, we subtract (2) from (1) to get:

0 = 3x => x = 0.

So the only set of solutions is (0, 1).

Method 3 (Gaussian elimination):

We can place this in an augmented matrix and row reduce.

\left[\begin{array}{cccc}1&5&1 & 1\n1&2&1 & 1\end{array}\right]

Row reducing this gives us:

\left[\begin{array}{cccc}1&5&1 & 1\n0&3&0 & 0\end{array}\right]

This tells us that the only solution for x is x = 0 (since we read this as "3x = 0") and thus, the only solution we get is (0, 1).

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = e^x^2 ln 4x^3

Answers

(d(lnx))/(dx)=(1)/(x)

Answer:

(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))

Step-by-step explanation:

We are given that a function

y=e^(x^2)ln(4x^3)

We have to differentiate w.r.t x

(dy)/(dx)=e^(x^2)* 2xln(4x^3)+e^(x^2)* (1)/(4x^3)* 12x^2

By using formula

(d(lnx))/(dx)=(1)/(x)

(d(e^x))/(dx)=e^x

(dy)/(dx)=e^(x^2)(2xln(4x^3)+(3)/(x))

(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))

Hence, the derivative of function

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Your salary is 2500 and you will be receiving a 2.5% pay increase this year. What will your new salary be?

Answers

Answer:

2562.50

Step-by-step explanation:

2.5=0.025

0.025*2500=62.50

2500+62.50=2562.50
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