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
Irina18 [472]
3 years ago
8

Now say we have an infinite sequence of independent random variables Xi (that is to say X1;X2;X3; ::::) with density f(x) stated

earlier. c. What is the probability that the first random variable/trial to be greater than 2 is on the 10 trial (first 9 trials are less than 2 and the 10 trial is greater than 2)
Mathematics
1 answer:
ycow [4]3 years ago
7 0

Answer:

a) The value of c that will make the density function a probability density function = 0.0430

b) P(X=2) = 0.387

P(X > 2) = 0.35475 = 0.355 to 3 s.f

c) The probability that the first random variable/trial to be greater than 2 is on the 10 trial (first 9 trials are less than 2 and the 10 trial is greater than 2) = 0.0000018125 = (1.8125 × 10⁻⁶)

The probability of getting a value greater than 2 on the 10th trial and getting a Value NOT greater than 2 on first 9 trials = 0.006878

d) 0.9806

Step-by-step explanation:

Continuous random variable X with density function f(x) = c (1 + x³) where c = constant

with a support SX = [0,3]

a) Value of c that will make the density function a valid probability density function.

A valid probability density function sums up to give 1 over the interval of its sample space. That is, the sum of the probabilities over its sample space equals 1.

P(U) = ∫³₀ f(x) dx = 1

∫³₀ c (1 + x³) dx = 1

c ∫³₀ (1 + x³) dx = 1

c [x + (x⁴/4)]³₀ = 1

c [3 + (3⁴/4)] = 1

23.25c = 1

c = (1/23.25)

c = 0.0430

The value of c that will make the density function a probability density function = 0.0430

b) Probability that X = 2

f(x) = 0.043 (1 + x³)

P(X=2) = f(2) = 0.043 (1 + 2³) = 0.043 (1 + 8)

P(X=2) = 0.043 × 9 = 0.387

Probability that X is greater than 2 = P(X > 2)

P(2 ≤ X ≤ 3) = ∫³₂ f(x) dx

P(2 ≤ X ≤ 3) = ∫³₂ 0.043 (1 + x³) dx

= 0.043 ∫³₂ (1 + x³) dx

= 0.043 [x + (x⁴/4)]³₂

= 0.043 {[3 + (3⁴/4)] - [2 + (2⁴/4)]}

= 0.043 {23.25 - 6}

= 0.043 × 17.25

P(2 ≤ X ≤ 3) = P(X ≥ 2) = 0.74175

P(X > 2) = P(X ≥ 2) - P(X=2)

= 0.74175 - 0.387 = 0.35475

c) the probability that the first random variable/trial to be greater than 2 is on the 10 trial (first 9 trials are less than 2 and the 10 trial is greater than 2)

P(X>2) = 0.35475

P(X<2) = 1 - P(X ≥ 2) = 1 - 0.74175 = 0.25825

The required probability = [P(X<2)]⁹ × [P(X>2)] = (0.25825)⁹ × (0.35475) = 0.0000018125 = (1.8125 × 10⁻⁶)

Although, this probability could also be interpreted as the probability of getting a Value greater than 2 on the 10th trial and getting a value NOT greater than 2 on first 9 trials.

P(X>2) = 0.35475

Probability of X not greater than 2 = P(X<2) + P(X=2) = 1 - 0.35475 = 0.64525

Required probability = [P(X≤2)]⁹ × P(X>2) = (0.64525)⁹ × 0.35475 = 0.006878

d) Probability that it will take less than 10 random variables/trials before we see a trial that is greater than 2?

This is a sum of probabilities from getting a trial greater than 2 on the first attempt to getting it on the 9th attempt (less than 10 trials)

P(X>2) = 0.35475

Probability of X not greater than 2 = P(X<2) + P(X=2) = 1 - 0.35475 = 0.64525

Required probability = [0.35475 + (0.64525)(0.35475) + (0.64525)²(0.35475) + (0.64525)³(0.35475) + (0.64525)⁴(0.35475) + (0.64525)⁵(0.35475) + (0.64525)⁶(0.35475) + (0.64525)⁷(0.35475) + (0.64525)⁸(0.35475)] = 0.980611147 = 0.9806

Hope this Helps!!!

You might be interested in
The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What
Oksana_A [137]

Using the domain concept, the restrictions on the domain of (u.v)(x) are given by:

A. u(x) ≠ 0 and v(x) ≠ 2.

<h3>What is the domain of a data-set?</h3>

The domain of a data-set is the set that contains all possible input values for the data-set.

To calculate u(x) x v(x) = (u.v)(x), we calculate the values of u and v and then multiply them, hence the restrictions for each have to be considered, which means that statement A is correct.

Summarizing, u cannot be calculated at x = 0, v cannot be calculated at x = 2, hence uv cannot be calculated for either x = 0 and x = 2.

More can be learned about the domain of a data-set at brainly.com/question/24374080

#SPJ1

3 0
2 years ago
1. You can buy a 6-hour phone card for $5.00, but the fine print says that each minute actually costs you 1.5 minutes of time. W
Vilka [71]
Divide 5.00 by 1.5 and you get (it's pretty long) 3.3333333333333333333333333333333

7 0
3 years ago
Evaluate - (2-6)(23).<br> O A. 8<br> O B.<br> 1<br> 8<br> Oc.<br> 1<br> 8<br> D. -8
kumpel [21]

Answer:

-92.

Step-by-step explanation:

2 - 6 is -4.

-4 x 23 is -92.

7 0
3 years ago
What is the value of x?<br> 16<br> 34
lord [1]

Answer:30

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Dashawn solves the following system of equations using the elimination method.
Liono4ka [1.6K]

Answer:

x = 4

Explanation:

3x - 4y = 36

5x + 2y = 8 ( multiply all by two )

3x - 4y = 36

10x + 4y = 16

13x = 52

Divide by 13

x = 4 hope this helps

6 0
3 years ago
Other questions:
  •  Amy​'s car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas s
    9·1 answer
  • What is 3 1\8 as a fraction in simplest form ?
    13·1 answer
  • How to solve 2/3x-36&gt;22
    15·1 answer
  • I WILL GIVE BRAINLIEST<br> x^2−2.2x+1.21&gt;0
    15·2 answers
  • What is the slope of the line that contains the points (-2, 2) and (3, 4)?
    11·2 answers
  • two cars traveled equal distances in different amounts of time. car a traveled the distance in 2.4 hours and car b traveled the
    5·1 answer
  • The cube of the difference of 1 and a number
    11·1 answer
  • HELP, it’s question 17
    7·2 answers
  • 1. identify the coeffieceint: 6x + 19
    5·2 answers
  • Find the product: 42.6 × 15.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!