0
votes
0answers
15 views

The critical value

I am facing a little problem is this question. Can somebody please help e here A sample of 500 drivers was asked whether or not they speed while driving. The following table gives a two-way ...
-1
votes
1answer
15 views

Probability math problem. [on hold]

Certain data obtained from a study of a group of 1000 subscribers to a certain magazine relating to their sex, marital status, and education were reported as follows: 312 males, 470 married, 525 ...
0
votes
3answers
24 views

The Objectivity of Statistical Testing

I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability $p$ of landing heads. We want to determine if our coin is truly fair - ...
0
votes
0answers
13 views

Calculating the critical value

I am facing a little problem is this question. Can somebody please help e here A sample of 500 drivers was asked whether or not they speed while driving. The following table gives a two-way ...
0
votes
1answer
28 views

Calculate Critical Value

Experience in investigating insurance claims shows that the average cost to process a claim is approximately normally distributed with a mean of 80 dollars. New cost-cutting measures were started and ...
1
vote
1answer
12 views

Hypothesis testing on minimum of exponentially distributed random variables

I am completely stuck with the following problem, because I do not know how to start: Let $X_1,...,X_n$ be independent and exponentially distributed with unknown parameter , and let ...
1
vote
0answers
21 views

Help with finding $E((\Phi(aX+b)^2))$ when $X$ is standard normal

I need help with calculating $$ E((\Phi(aX+b))^2)=\int_{-\infty}^\infty (\Phi(ax+b))^2\phi(x)dx $$ where $X$ is a standard normal random variable and $a$ and $b$ are constants. $\Phi$ and $\phi$ ...
1
vote
1answer
19 views

$MLE$ of $\theta$ when $X_1 , X_2 , …, X_n$ is a sample with pdf $f(x, \theta) = e^{\theta - x}; x \ge \theta$

How can we find the $MLE$ of $\theta$ when $X_1 , X_2 , ..., X_n$ is a sample with pdf $f(x, \theta) = e^{\theta - x}; x \ge \theta$ ? $L(\theta) = \prod_{i = 1}^{n} e^{\theta - x_{i}}$ $L(\theta) = ...
0
votes
0answers
10 views

How large a sample will need to be taken to meet the administrator's needs?

A hospital administrator wants to measure average time per hip replacement procedure performed in the institution's operating suite. He is willing to be within 10 minutes of the true value with a ...
1
vote
1answer
20 views

If I have a random variable X with a given Probability Density Function, How do I find the PDF of the area of a circle with radius X?

To find the PDF of the area of the circle, do I just substitute the PDF of the random variable X in for the radius in the circle area equation?
0
votes
1answer
16 views

Calculating confidence interval - formula

I have the following problem that I get the feeling I'm mixing formulas. ...
0
votes
1answer
8 views

class conditionals and priors

Let's say we have an event A that indicates whether an image contains a person or not. A = 1 indicates that the the image contains a person and z = 0 means that it does not. Assume that L which can ...
1
vote
1answer
63 views

Card probability

There are two 10-card decks, consisting of 5 red cards and 5 blue cards each. Both are shuffled separately. One card is then dealt from each deck and compared. This is repeated for all 10 pairs of ...
1
vote
2answers
29 views
0
votes
1answer
17 views

Alternative Hypothesis

I am facing a little problem is this question. Can somebody please help e here A sample of 500 drivers was asked whether or not they speed while driving. The following table gives a two-way ...
1
vote
1answer
9 views

Self-Selection Bias Intrinsic to Survey Samples?

I'm new to stats so bear with me in asking this question. I'm sure my novice will shine through. I've noticed that with any survey there is an intrinsic opportunity for self-selection bias (There is ...
1
vote
1answer
31 views

Null Hypothesis

Experience in investigating insurance claims shows that the average cost to process a claim is approximately normally distributed with a mean of 80 dollars. New cost-cutting measures were started and ...
0
votes
1answer
33 views

Lickly hood estimators and discrete random var

If have discrete random variable X and have the observations that X=1, twice, X=3, once and X=4, six times is the likely hood of these observations, L = P(X=1)^2 . P(X=3)^1 . P(X=4)^6 or L = ...
0
votes
1answer
17 views

Approximating the expectation of a function with sampling

I'm reading a paper (section 5.1) that approximated the expected value of a function $f(X,Y)$ of two random variables using Gibbs sampling. As far as I know the expectation of $f(X,Y)$ is defined to ...
0
votes
1answer
6 views

Variences and adding them from independent random variables?

If I have 3 random varibles X, Y and Z and X=Y+Z then var(X)=var(Y)+var(Z), but Y=X-Z therefore var(Y)=var(X)+var(Z), it is clear that these two contridict, so what makes one of them right and the ...
0
votes
1answer
19 views

Lack of memory property of probability distributions

According to wikipedia lack of memory property applies to geometric and exponential distributions. I was trying to apply it to binomial distribution. Am I modelling my question correctly? So imagine ...
1
vote
3answers
832 views

Probability of Parking Spot Being Empty

A parking spot is unoccupied 1/3 of the time... But, you find it empty for nine consecutive days in a row. Find the probability that it will be empty on the tenth day. Read more: ...
1
vote
1answer
12 views

Derive the Cramer-Rao lower bound (CRLB) for any unbiased estimator of $\mu^2$.

Let $Y_1, Y_2, . . . , Y_n$be a random sample from a normal distribution with mean μ and variance 1. Derive the Cramer-Rao lower bound (CRLB) for any unbiased estimator of $\mu^2$. Could anyone ...
0
votes
1answer
19 views

Sum of two independent non-identical uniform random variables

Let's say we have two independent random variables, $X$ is uniform on $[0,1/2]$ and $Y$ is uniform on $[1/2,1]$. If we look at the distribution of $X+Y$, is it triangular distribution between ...
0
votes
0answers
12 views

Questions related to Rao–Blackwell theorem

In this exercise, we illustrate the direct use of the Rao–Blackwell theorem. Let $Y_1, Y_2, . . . , Y_n$ be independent Bernoulli random variables with $p(y_i | p) = py_i (1 − p)1−y_i , y_i = 0, 1.$ ...
1
vote
0answers
27 views

find E($\bar{Y^4})$ by using moment generating function for a normal distribution with mean μ and variance 1.

Let $Y_1, Y_2, . . . , Y_n$be a random sample from a normal distribution with mean μ and variance 1. I would like to find E($\bar{Y^4})$ by using moment generating function. The setup I have right ...
1
vote
1answer
19 views

Calculate the Marginal Probability

f($X_1$, $X_2$| $p_1$, $p_2$) = $p_1^{x_1}$(1-$p_1)^{({n_1}-{x_1})}$$p_2^{x_2}$(1-$p_2)^{({n_2}-{x_2})}$ $p_1$~Unif(0,1) independently $p_2$~Unif(0,1) $n_1$=34 $n_2$=56 Calculate the marginal ...
0
votes
1answer
15 views

Moment Generating Function of the Chi-Squared Distribution

The questions wants us to show that the MGF for the chi-squared distribution is equal to I know that to show that I need to evaluate this integral. I'm not sure where to begin to evaluate it. ...
1
vote
0answers
42 views

Need help finding probability distribution [on hold]

In Cairo $30\%$ of residents listen to the local fm radio. $10$ residents are chosen at random: a) state the distribution of the random variable b) find the smallest value of $s$ so that $\Pr(X \ge ...
1
vote
0answers
20 views

Find critical Value

A Basketball scout randomly selected 144 players and timed how long each player took to perform a certain drill.The times in this sample were distributed with a mean of 8 minutes. The population ...
0
votes
0answers
33 views

Probability of events [on hold]

1) 5 cards are selected from a 52-card deck for a poker hand. a) How many simple events are in the sample space? b) A royal flush is a hand that contains the A,K,Q,J, and 10, all in the same suit. ...
0
votes
1answer
21 views

Likelihood of Two Binomial Distributed RV's

We are given that Let X1~Bin(n1 = 34, p1) and X2~Bin(n2 = 56, p2) In general, what is the likelihood, L(p1, p2) = f (X1, X2 | p1, p2) for the data X1 and X2 I believe that I am supposed to use a ...
0
votes
1answer
17 views

Functional Choice for p in a Bernoulli Distribution

Why is the functional choice $p = \exp(x)/(1+\exp(x))$ to model $p$ a good one in a Bernoulli distribution? Is it because it is limited at $0$ as $x$ approaches $0$ and $1$ as $x$ approaches ...
1
vote
1answer
30 views

probability and applied statistics 3 [on hold]

given two urns, suppose urn 1 contains four black and seven white balls. urn 2 contains three black , one white , and four yellow balls . we select an urn at random and then draw a ball . what is the ...
2
votes
2answers
83 views

Unbalanced game: probability of winning over an infinite number of possible match sequences

We have 2 players, A and B, competing. The probability that A wins a match is p, making the probability that B wins a match (1-p) = q. The game is won by player A as soon as he gets one more win than ...
1
vote
2answers
57 views

Forth Moment of Sum of Normal with Equal Correlation

I have $X_1,\dots,X_n$ identically normal distributed $N(0,\sigma^2)$ and $\operatorname{corr}(X_i,X_j)=\rho $ for all $i\neq j$. I'd like to compute \begin{equation} E\left(\sum_{i=1}^nX_i\right)^4. ...
4
votes
1answer
31 views

If $X$ ~$Uni(-1,1)$ show that $X$ and $X^2$ are not independent

I provide my approach in solving this but I amd not entirely sure whether I am correct. Since X~uni(-1,1) $f_X(x)=1/2$ and $F_X(x)=(x+1)/2$. $F_{X^2}(x)$=$Pr[X^2≤x]$=$2F_X(√x)$=$(√x+1)/2$. Hence ...
0
votes
0answers
15 views

confidence coefficient z value

I'm having a bit of difficulty understanding a concept in my notes and was wondering if someone could help me. This is probably a really simple concept that I've just completely overcomplicated but ...
0
votes
1answer
31 views

Clique factorization

I'm reading about Clique factorization in wikipedia: http://en.wikipedia.org/wiki/Gibbs_random_field#Clique_factorization but I'm unable to understand this: What is $X_C$ here? Ok I understood ...
1
vote
2answers
45 views

Probability, chose two skittles, out of 2 skittles left from a bag of skittles with 5 colors.

so me and my friend are studying statistics but we are just stuck on this stupid skittle question we made up ourselves when we tried to guess the colors of the two last skittles so we can see who will ...
0
votes
1answer
19 views

Probability and Standard Deviation

Hey I'm confused about how to do this kind of problem. I can't figure out how to find the standard deviation. There are on average 4 tetanus cases reported in the US each month. What is the ...
0
votes
1answer
27 views

Covariance of two values

A fair die is rolled twice (independently). Let X1 and X2 be the numbers resulting from the first and second rolls, respectively. Define Y=X1+X2 and Z=4⋅X1−X2. Find the covariance between Y and Z. ...
0
votes
1answer
34 views

Help in Stats, Joint p.d.f

Let $X$ and $Y$ be random variables that have a joint p.d.f., which is given by the formula $\displaystyle p_{X,Y}(x,y)=\frac{5e^{−5x}}{x}$ when $0< y < x < \infty$, and $p_{X,Y}(x,y)=0$ for ...
0
votes
0answers
9 views

Factorizing about an undirected graph [closed]

When do we say that a distribution factorizes about an undirected graph $G$ with maximal cliques $C$?
1
vote
1answer
37 views

Hammersley–Clifford theorem

I'm reading this paper http://image.diku.dk/igel/paper/AItRBM-proof.pdf and I got stuck in page 4 with equation (1) that's based on Hammersley–Clifford theorem. I'm not good in reading set theory ...
0
votes
1answer
39 views

Joint p.d.f stats help [on hold]

$X$ and $Y$ are random variables that have a joint p.d.f., given by $p(x,y)=cx^9y^6$ when $0\le x,y\le 1$ and $p(x,y)=0$ for all other $x,y$. Here $c\ge0$ is a constant, which you should find. What ...
-1
votes
1answer
96 views

jointly normally distributed random variables [on hold]

Suppose that X and Y are jointly normally distributed random variables, each of which is standard normal, and the correlation coefficient between X and Y is equal to 0.4. Find the probability that ...
0
votes
1answer
46 views

Joint PDF and Conditional PDF [on hold]

$X$ and $Y$ are random variables that have a joint pdf, given by $p_{X,Y}(x,y)=4xe^{-x(y+4)}$ when $x,y>0$ and $\ p_{X,Y}(x,y)=0$ for all other $x,y$. Find a formula for the conditional pdf $\ ...
0
votes
1answer
16 views

Example of dependent but conditional independent

There are a lot of events that are independent and conditional independent. Is there any events that are dependent but conditionally independent?
0
votes
1answer
37 views

How to come up with a probability distribution knowing the mean value? [closed]

I would like to know about some algorithms or techniques to find a discrete probability distribution knowing the mean value. Let's say given the mean=2.5. The probability distribution can be $x_1=2, ...