This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under ...

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1answer
25 views

Finding the distribution of $Y_2$,knowing that $Y_1 \in Po(\lambda/2)$

The random variables $N,X_1,X_2..$ are independent, $N\in Po(\lambda)$, and $X_k \in B(1/2) , k \geq 1$ Set. $Y_1 =\sum\limits_{k=1}^{N}X_k $ and $Y_2 = N - Y_1$. Determine the distributions of ...
0
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0answers
24 views

How to divide set of numbers [closed]

$A = \left\{a1, a2, \ldots, a_N\right\}$ is a set of $n$ numbers elements (positive integers) and must be divided into $K$ subsets in order so that the sum of all elements in each subset are equal to ...
0
votes
2answers
16 views

Dependence of random variables

I need to solve the following problem: Let X be a normal random variable with mean  and standard deviation  and let I, independent of X, be such that P{I = 2} = P{I = -2} = 0.5. Let Y = I X. In ...
0
votes
1answer
13 views

One parent is a cystic fibrosis carrier, and the other has no cystic fibrosis gene

One parent is a cystic fibrosis carrier, and the other has no cystic fibrosis gene. Find the probability of each of the following. (a) The child would have cystic fibrosis. Answer = 1/4 = 0.25 (b) ...
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3answers
37 views

P(A|B^c) given the following

Given $P(A) = 0.2, P(B) = 0.6$, where A and B are mutually exclusive, find the conditional probability $P(A|B^c)$. How do I determine this answer? I've been trying to figure it out for hours.
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1answer
18 views

Conditional Probability of two random variables

A fair coin is tossed with the outcome mapped into $X = 1$ for a head and $X = 0$ for a tail. If it comes up heads, then a fair die is tossed. The outcome of the die is denoted by $Y$ and is set equal ...
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0answers
23 views

Probability of James Choosing Earlier Train Than Bill

James can choose to catch either train 1 or train 2. But Bill can choose to catch either Train 1, 2, 3 or 4. Both James and Bill choose their train at random. What is the probability that James ...
0
votes
1answer
15 views

Probability Mass Function and expected value

Voice calls cost 0.20 cent each and data calls cost 0.30 cent each. C is the cost of one telephone call. The probability that a call is a voice call is P[V] = 0.6. The probability of a data call is ...
0
votes
1answer
24 views

Probability - Random viarbles

A notepad manufacturer requires that 90% of the production is of sufficient quality. To check this, 12 computers are chosen at random every day and tested thoroughly. The day's production is deemed ...
1
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0answers
18 views

Approximate Solution to Backwards Recurrence of Dynamic Game

Suppose we keep tossing a fair dice until we reach some cumulative sum greater than or equal to $N$. Then, let $S_k$ be the expected value of the final sum, given that the current sum is $k$. We have ...
3
votes
2answers
112 views

Probability that each bucket has $\geq 3$ balls

There are $30$ buckets. John throws $20$ balls, each time landing uniformly among the buckets. What is the probability that no bucket contains $\geq 3$ balls? If the question were $\geq 2$ balls, we ...
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1answer
27 views

Question in permutations

When we use this law? And in any case we use it? Thank you and I wish clarification.
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0answers
24 views

Pairing two types of balls by color [closed]

I have 150 plastic and 150 metal balls in 149 different colors. I've picked a random 50 plastic and 50 metal balls. I pair the balls by color. How many pairs can I make? Thanks for any suggestions!
0
votes
0answers
33 views

Understanding what $P - P \log(P)$ means for an event of probability $P$

Let $(\Omega, \Sigma, \mathbb{P})$ be a probability space, $X$ be a random variable, and $E \in \Sigma$ be an event with $\mathbb{P}(E) = P$. Then $P - P \log(P) \in [0, 1]$, for all $P \in (0, 1]$, ...
0
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1answer
18 views

Random variables with all moments. Is this statement true?

Let $X$ be a random variable such thta $X\neq 0$, $P$-a.s. Then $$X\in \bigcap_{p\geq 1} L^p(\Omega) \iff \frac{1}{X} \bigcap_{p\geq 1} L^p(\Omega).$$ In other words, is the space $\bigcap_{p\geq 1} ...
0
votes
1answer
16 views

Which of two distributions was sampled from?

Suppose that I have two sets $A$ and $B$. each of which contains $N$ random variables. Set $A$ has $N$ normal random variables all with the same mean $\hat{\mu}$ and variance $\hat{\sigma}$. Set ...
1
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1answer
35 views

If X and Y are independent, then $\sigma(X)$ and $\sigma(Y)$ are

I want to show the following: If X and Y are independent, then their generated sigma-algebras $\sigma(X)$ and $\sigma(Y)$ are independent. Let $A \in \sigma(X)$ and $B\in\sigma(Y)$ be arbitrary. ...
1
vote
2answers
38 views

Dice: Probability of rolling a number between two other dice throws

I was pretty suprised about this problem when I encountered it in one of my excercise sheets and would like to ask for an approach here because I have no idea how I'm supposed to get started here: ...
0
votes
1answer
18 views

Probability with Bayes rule

Manufacturer of cheap computers makes a requirement to the production that $90\%$ of the computers need to meet the quality requirements. To test that he takes $12$ random computers of the production ...
0
votes
1answer
23 views

complements questions [closed]

Find $P(A\cup (B^c \cup C^c)^c)$ if events A,B,C are mutually exclusive and $P(A)= \frac{3}{7}$.
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1answer
25 views

Infinite boundary for random variables

I have a question Suppose that X and Y are random variables with joint pdf is given by and zero otherwise. I need to find marginal and conditional pdf's.But I don't know how to intagrate over an ...
0
votes
1answer
15 views

Joint distribution of two random variables

I have a question about joint distributions but couldn't find the solution. Suppose that $X$ and $Y$ are two random variables and their joint pdf is given by $$f_{XY}(x,y)=cxy(1-x-y), ...
2
votes
2answers
68 views

Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$

Let $A$ and $B$ be two events of a probability space. Prove that $\displaystyle|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$ I think it's a very challenging problem, and I've made no progress so far ... ...
0
votes
1answer
18 views

a conductor wishes to build 9 houses, each different in

a conductor wishes to build 9 houses, each different in design.in how many ways can he place these homes on a street if 6 lots are on one side of the street and 3 lots are on another side? answer ...
0
votes
1answer
35 views

Battery lifetime as normal distribution?

I want to model battery lifetime, which decrements continuously at every epoch (i.e., work-cycle) in the following way. So it takes values such as 100, 99.7, 99.3, 99.2, ... 0 (a continuous random ...
0
votes
1answer
48 views

Probability question - statistics

 Could somebody please help me, I have been trying to calculate this problem all day, but with no success. Here is the problem: "A teacher was asked by her principal to select 7 students at random ...
0
votes
1answer
38 views

95 percent of satellites launched are successful. What's the probability that,the next four launches, there will be no mishaps and exactly one mishap? [closed]

I honestly have no clue how to do this. Any help would be appreciated. I have tried everything.
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1answer
27 views

Binomial Probability (Dice)

The throwing of a one or two is called a success. The six dice are thrown together 64 times and the frequencies of the throws with 0, 1, 2,..., 6 successes are summed over all six pairs are as ...
0
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2answers
30 views

Estimating P(X $\ge$ k) with Chebyshev's inequality

I have managed to derive non-rigorously that P(|X - E[X]| $\ge$ a) $\le$ $\frac{E[X - E[X]|^2}{a^2}$. for a random variable X. Now let X be a random variable with Poisson distribution, with mean ...
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votes
1answer
77 views

A baseball player's batting average is $0.31$. If, in a given game, [closed]

he bats four times, what is the probability that he will get: no hits? at most two hits? at least two hits?
0
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0answers
38 views

If $Y=X\beta+\epsilon$, prove that the least square estimator $\hat\beta$ is independent of $Y-X\hat{\beta}$

Let $Y=X\beta+\epsilon$, where $Y$ is an $n$ by $1$ vector, $X$ is an $n$ by $p$ matrix with full rank and $\epsilon$ is an $n$ by 1 vector of random errors independently and normally distribution ...
1
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1answer
23 views

Probability of Type I Error with Poisson Distribution

In a homework problem, I am given a Poisson distribution with lambda = 1 as null hypothesis, lambda greater than or equal to 2 as an alternate hypothesis, and 3 as a test statistic. I am instructed to ...
1
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1answer
15 views

Find the conditional distribution ,which probably is binomial

Sheila has a coin with $P(head)= p_1$ and betty has a coin with $P(head) = p_2$.Sheila tosses her coin $m$ times. Each time she obtains heads , betty tosses her coin(otherwise not). Find the ...
1
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1answer
22 views

question: A jar on your desk contains twelve black, nine red,

1-A jar on your desk contains 12 black, 9 red, 9 yellow, and 5 green jellybeans. You pick a jellybean without looking. Find the odds of picking a black jellybean. my Answer 12/35 2-A jar on your ...
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2answers
70 views

How come probabilities can't be more than 100%? [closed]

I'm just wondering why probabilities can't go over 100%. I really hope this is a good question to ask. Also, I want to hear your "probable" answers (I'm funny, aren't I?)! Good luck! The coast is ...
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votes
2answers
75 views

“Back to square one” problem

There's a problem I've been stuck on in preparation for junior programming contest I'm going to participate in. It is as follows: The "back to square one" problem is played on a board that has ...
0
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2answers
37 views

Show that if X is a continuous random variable on $[b,\infty)$ then $\mathrm{E}[X]=b+\int_b^{\infty}(1- F(x))dx $

I have to use the definition $$\mathrm{E}[X]=\int_{-\infty}^{\infty}xf(x)dx $$ and integration by parts. I haven't done an improper integral in a while, so I'm pretty from the beginning that I made a ...
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0answers
59 views

Probability question in statistics [closed]

Suppose I give you a list of 24 problems to study, from which I will randomly pick 14 questions for your first midterm exam. For whatever reason, you prepare for the midterm exam by completing and ...
1
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1answer
30 views

Probability involing percentages (Bernoulli?)

Assume that about 56% of population belong to group type of O. A) What is the probability that it will need to take a blood test from exactly three individuals in order to find a person with O-type ...
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votes
1answer
16 views

Can someone solve this probability question and tell me the steps? [closed]

A fair coin is tossed 9 times. What is the probability that: a) Exactly 7 heads appear? So what I tried to do was 9!/7!2! but I guess I was incorrect b) At least two heads appear? c) At ...
1
vote
1answer
26 views

What are the continuous functions that satisfy the following?

$f(x) = \begin{cases} 0, & x < 0 \\ 1 - f\left(\dfrac{1}{x}\right), & x > 0\text{.} \end{cases}$ I want this to generate a random variable that will be used as a proportion in a way ...
0
votes
2answers
47 views

$3$ different balls placed randomly in potentially $3$ different initially empty boxes.

You have $3$ different balls and you put them at random in potentially $3$ different initially empty boxes meaning any box can hold anywhere between $0$ to $3$ balls (inclusive). Assume once the ball ...
-1
votes
1answer
13 views

probability distribution

I would really be grateful if someone could answer me promptly. I believe i should use the poisson distribution model because that is the suitable one however i cannot satisfy the condition of ...
0
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2answers
38 views

Statistic question (probability)

A suburban town is made up of 36 % low-income 43 % medium-income, and 21 % high-income households. It is known that 82 % of the low-income, 55 % of the medium- income, and 2 % of the ...
0
votes
1answer
17 views

How to combine dependent probabilities?

Assume there are 3 types of events: E1, E2 and E3. Probability that E3 happens if E1 happened is P1. Probability that E3 happens if E2 happened is P2. Let's assume E1 and E2 are independent events. ...
1
vote
1answer
39 views

Counting and probability gift exchange problem

There are 50 people (numbered 1 to 50) and 50 identically wrapped presents around a table at a party. Each present contains an integer dollar amount from $1 to $50, and no two presents contain the ...
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votes
1answer
31 views

Probability Question in Statistic

Individuals in a certain population have a $39\%$ probability of contracting disease $A$ and a $21 \%$ probability of contracting disease $B$, and a probability of $4\%$ of contracting both diseases ...
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votes
5answers
65 views

Guessing on the SATs, is it ever better to leave it blank than to guess?

On most SAT questions, there are 5 answers of which exactly one is correct and exactly four are wrong. If one answers correctly you get $1$ point. If you answer incorrectly, you receive $-\frac14$ ...
0
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2answers
31 views

Probability, why is this wrong? (Combinations and Permuations)

Why is this the wrong approach to solve this problem? "There are 65 students. 20 of them are sophomores, 20 are freshmen, 15 are juniors and 10 are seniors. When picking a 4 student committee, ...
0
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2answers
17 views

What is the average number of steps to reach a destination?

Lets say that a system has $3$ steps and the probability of going to $$\text{STEP}_1\longrightarrow \text{STEP}_2 \quad\text{ is }\, 0.5\phantom{0}$$ and that of $$\text{STEP}_2\longrightarrow ...