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![### Probability Distribution Problem
**6.** Suppose \( X \) has a probability mass function (p.m.f.) given by:
\[
P(X = n) = \frac{1}{n(n+1)}
\]
for \( n \in \mathbb{N} \).
#### Tasks:
**(a)** Compute \( P(X > n) \) for \( n \in \mathbb{N}_0 \).
**(b)** Compute the mean of \( X \). (You may find the answer unsettling. This distribution has a heavy upper tail.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9e27b5d-0ab8-428e-954d-97d64fc14c61%2F8f00bd44-dcca-4187-a0a9-a41dc9c70d69%2Fcwpa7p_processed.png&w=3840&q=75)
The probability mass function of X is given as follows:
.............(I)
Step by step
Solved in 3 steps
- The profits of a mobile company are normally distributed with Mean of R.O (180) and standard deviatic of R.O (8). a. Find the probability that a randomly selected mobile has a profit greaterthan R.O ( 190). b. Any mobile phone which profit is greater than R.O (190) is defined as expensive. Find the probability that a randomly selected mobile has aprofit greaterthan R.O ( (200) given that it is expensive. Half of expensivemobile phones have aprofit greaterthan R.O h. Find the value of h. C.Q2. The sampling distribution of means tends toward Normality only when the underlying populations is Normal. This is true of Central Limit Theorem. TrueB. FalseC. None of the above12. The number of new individuals in a population of animals is sometimes approximated calculating the expected number of survivors of the new born animals from the next genera- tion. The idea is that the number of new animals born follows some probability distribution, and the number of animals that survive depend on how many are present.¹ One example of a survivor function is the following: S₁(k) = b.ck, where b and c are real numbers with 0Let X have an exponential distribution with a mean 10. Compute P(102A. X is normally distributed with a mean of 8 and standard devaition is of 0.5. Determine P(8.44(less than or equal to)X)Suppose that you enter a fantasy baseball league. Suppose that the 2021 team budget, say , is randomly drawn from a uniform distribution on the interval , where the unit is U.S. million dollars. In addition, suppose that after the value has been observed , the 2022 team budget, say , is randomly drawn from a uniform distribution on the interval . In other words, the 2022 budget is at most as large as the 2021 budget. a) For any given value of x(50<x<350), obtain E[Y|X=x] b) In view of part (a), obtain E[Y|X] c) Atlanta Braves won the 2021 World Series title. Their estimated 2022 payroll is about $130 million. Would your 2022 fantasy baseball budget be on average larger than their 2022 payroll? Explain briefly.Births are approximately Uniformly distributed among the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks). 1. а. What is the probability distribution for X? For parts b – g include functions and shaded graphs b. Find the probability that a person is born at the exact moment week 19 starts Find the P(25.2.1 The conditional probability distribution of Y given X = x is fy.0) = xe-y for y> 0, and the marginal probability distribution of X is a continuous uniform distribution over 0 to 10. a. Graph fyv) = xe¬w for y > 0 for several values of x. Determine: b. P(Y < 2|X = 2) d. E(Y |X = x) f. fr(y) c. E(Y | X = 2) e. fxy(x, y)4.Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON