1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
deff fn [24]
3 years ago
7

Two faulty machines, M1 and M2, are repeatedly run synchronously in parallel (i.e., both machines execute one run, then both exe

cute a second run, and so on). On each run, M1 fails with probability p1 and M2 fails with probability p2, all failure events being independent. Let the random variables X1, X2 denote the number of runs until the first failure of M1, M2 respectively; thus X1, X2 have geometric distributions with parameters p1, p2 respectively. Let X denote the number of runs until the first failure of either machine. Compute the distribution of X. What is its expectation?
Mathematics
1 answer:
leonid [27]3 years ago
7 0

The event that either M1 or M2 fails has probability

P(M_1\text{ fails or }M_2\text{ fails})=P(M_1\text{ fails})+P(M_2\text{ fails})-P(M_1\text{ and }M_2\text{ both fail})

by the addition rule. Failure events are independent, so

P(M_1\text{ and }M_2\text{ both fail})=P(M_1\text{ fails})P(M_2\text{ fails})

so that

P(M_1\text{ fails or }M_2\text{ fails})=p_1+p_2-p_1p_2

Denote this probability by p. Then X follows a geometric distribution with this parameter p and has density

P(X=x)=\begin{cases}(1-p)^{x-1}p&\text{for }x\ge1\\0&\text{otherwise}\end{cases}

The expectation is \dfrac1p=\dfrac1{p_1+p_2-p_1p_2}.

You might be interested in
Write a function to represent the set of ordered pairs.<br> {(2, 2), (3,7). (4, 14), (5,23)}
MrMuchimi

Answer:

Step-by-step explanation:

The set of ordered pairs {(1 , 7) , (−1 , 7) , (8 , −6) , (−3 , 2)} is a function

The set of ordered pairs {(4 , 7) , (−1 , 2) , (4 , −6) , (−3 , −2)} is not a

function

The set of ordered pairs {(3 , 7) , (−1 , 2) , (−4 , −2) , (−3 , −2)} is a function

The set of ordered pairs {(−3 , 7) , (1 , 2) , (4 ,−2) , (12,−4)} is a function

An ordered pair represents a relationship between two values

The first value is the input the second value is the output

1. A relation is a set of inputs and outputs

2. A function is a relation with one output for each input

3. All functions are relations

{(1 , 7) , (−1 , 7) , (8 , −6) , (−3 , 2)}

∵ Each x-coordinate in each ordered pair has only one y-coordinate

∴ The relation above is a function

The set of ordered pairs {(1 , 7) , (−1 , 7) , (8 , −6) , (−3 , 2)} is a function

{(4 , 7) , (−1 , 2) , (4 , −6) , (−3 , −2)}

∵ The x-coordinate 4 has two values of y (7 and -6)

∴ The relation above is not a function

The set of ordered pairs {(4 , 7) , (−1 , 2) , (4 , −6) , (−3 , −2)} is not a

function

{(3 , 7) , (−1 , 2) , (−4 , −2) , (−3 , −2)}

∵ Each x-coordinate in each ordered pair has only one y-coordinate

∴ The relation above is a function

The set of ordered pairs {(3 , 7) , (−1 , 2) , (−4 , −2) , (−3 , −2)} is a function

{(−3 , 7) , (1 , 2) , (4 ,−2) , (12,−4)}

∵ Each x-coordinate in each ordered pair has only one y-coordinate

∴ The relation above is a function

The set of ordered pairs {(−3 , 7) , (1 , 2) , (4 ,−2) , (12,−4)} is a function

6 0
3 years ago
Monica has $4.75 on her
Aleksandr [31]

Answer:

6

4.75÷.75=6

3.25÷.50=6

6 0
2 years ago
I don’t know how to solve this it’s exponents.
matrenka [14]

Answer:

9^6

Step-by-step explanation:

When dividing exponents with the same base, we subtract the exponents

a^b/ a^c = a^(b-c)

9^11/9^5 = 9^(11-5)

              = 9^6

4 0
2 years ago
Which set of parametric equations over the interval 0 ≤ t ≤ 1 defines a line segment with initial point (–5, 3) and terminal poi
Ksivusya [100]

Given:

A line segment with initial point (–5, 3) and terminal point (1, –6).

To find:

The set of parametric equations over the interval 0 ≤ t ≤ 1 which defines the given line segment.

Solution:

Initial point is (–5, 3). So,

x(0)=-5,y(0)=3

Terminal point is (1, –6).

x(1)=1,y(1)=-6

Check which of the given set of parametric equations satisfy x(0)=-5,y(0)=3,x(1)=1,y(1)=-6.

Put t=1 in each set of parametric equations.

In option A,

y(1)=3-6(1)=3-6=-3\neq -6

So, option A is incorrect.

In option B,

y(1)=1-6(1)=1-6=-5\neq -6

So, option B is incorrect.

In option C,

y(1)=3-9(1)=3-9=-6

x(1)=-5+6(1)=-5+6=1

Put t=0, in this set of parametric equations.

x(0)=-5+6(0)=-5

y(0)=3-9(0)=3

So, option C is correct.

In option D,

y(1)=1-7(1)=1-7=-3\neq -6

x(1)=-5+8(1)=-5+8=3\neq 1

So, option D is incorrect.

8 0
3 years ago
Suppose a simple random sample of size n = 1000 is obtained from a population whose size is N = 2,000,000 and whose population p
faltersainse [42]

Answer:

p(x\geq 520)  = 0.0293

Step-by-step explanation:

Given data:

random sample size n = 1000

Population size is N - 2,000,000

P = 0.49

We know

\sigma_p = \sqrt{\frac{p*(1-p)}{n}}

\sigma_ p = \sqrt{\frac{0.49*(1-0.49)}{1000}} = 0.0158

Probability for having X =520

sample proportion \hat p = \frac{520}{1000} = 0.52

p(x\geq 520)  = P(\hat p\geq)

                       = P(Z\geq \frac{0.52 - 0.49}{0.0158})

                       = P(Z\geq 1.89) = 0.0293

p(x\geq 520)  = 0.0293

6 0
2 years ago
Read 2 more answers
Other questions:
  • To the nearest tenth of a degree, find the sizes of the acute angles in the 5-12-13 triangle and in the 9-12-15 triangle. This e
    14·1 answer
  • You buy a computer for $1200. The value of the computer decreases by 30% each year. Find the value of the computer after 4 years
    10·1 answer
  • Translation of the length of a rectangle is 2 feet greater than twice its width. If the perimeter is 25 feet, fine the width
    7·1 answer
  • What system shows the correct numbers to multiply by the coefficients in order to eliminate y from the first two
    14·1 answer
  • Y=4x-200
    7·1 answer
  • Joshua is planning to make a large consumer purchase. If the item costs x dollars in his home state of West Virginia, where the
    8·1 answer
  • Can someone please answer my question for real please. I’ll give extra points
    10·1 answer
  • A=7.5<br> B=30<br> C=15 square of 2<br> D= 15
    6·1 answer
  • 5 times 4 times 2 times 2 divided by 2 minus 4​
    13·1 answer
  • Do rational numbers have to be whole numbers?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!