expected value

The chi-square distribution is defined as the distribution of Y = X_1**2 + X_2**2 + ... + X_k**2 with X_i independent standard normally distributed (mean 0, std 1). The expected value of a sum of variables is E(X_1 + X_2) = E(X_1) + E(X_2) The expected value of a product of independent...

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Hi, I am very puzzled as to how they achieved μ=2/5 in the example below. I understand that μ is just expected value which would mean summing x or y with its possible realizations. I'm thinking this is very obvious, however, I just can't see how they arrived at 2/5, which just proves I...

We throw the coin 1 000 000 times. How many times on average will make 13 successful heads? Now the problem with the naive: 1 000 000/(2^13) is that once it made 13 heads the 14 head will happen with 1/2 probability , but it will count as 2 13 successful heads. 15 will happen 4xtimes less, but...

What I have done so far: If the student was expected to make a 75%, we basically expected he would get 15 of the 20 questions correct. Now that he has misbubbled his answers, we expect those 15 he should've gotten right to now be wrong. For the remaining questions he now has a 1/10 chance of...

Hi everyone - see my problem below. With a regular die I know my denominator is 36 for each probability. What I'm wondering here is if that changes since multiple sides of the die have the same number... Right now I have the probability of a sum of 2 is 1/36, a sum of 3 as 2/36, sum of 4 as...

Hi guys just a quick question I am told i have two values which are 100 with probability of 0.8 and 1000 with probability of 0.2. Now, I know the E(X) is just 100(.8) + 1000 (.2). I know my var(x) = e(x^2) - e(x)^2 so is my var(x) just 100^2(.8) and 1000^(.2) ?

It is given: If you succeed to solve a Sudoku with probability 0.4 and you try many times, how likely is it that you succeed twice before you fail 5 times? What is the expected number of failures before two successes? I don't understand which one between the binomial, geometric, negative...

I need to determine the distribution function of an exponential random variable with mean 2, given that its outcome is larger than 2 and give the resulting expected value? I know that the mean is 1/lambda, so lambda should be 1/2. I get that way 0.5*e^(-0.5x) >= 2. How can I deal with the...

A dise is claimed to be biadsed that the probability of rolling a 3 is higher than that of the rest of the numbers. 1. What is standard desfviation of the # of times that a 3 is expdected to be rolled in 20 rolls of the dice. 2. Is the die biadsed?

I'm having a hard time figuring out what the expected value of Y = max(X1, X2, X3, ... , Xn) with pdf (x;θ) = 2x/θ^2. So it is the nth value of order statistics Y1<Y2<Y3.....<Yn. Does anyone know?

Hi all, I'm solving the problems in probability but, the question below looks simple but quite confusing to me. Regarding question 2-(c), any tips or advice would be appreciated to me. 2. Suppose that we have N balls numbered 1 to N. If we let Xi be the number on the ith drawn ball so...

I am trying to determine for Y people selecting from X restaurants (with an equal probability) what the expected value of the number of restaurants chosen would be. All decisions are independent. Ex: 2 people and 2 restaurants - E(X) = 1(.5) + 2(.5) = 1.5 restaurants will be visited on...

Violations 0 0 1 2 3 4 5 >5 Fine A$1000 0 0 10 10 10 20 50 (Please note from the table that 0 violations = 0 fines, 1 violation = 0 fines, 2 violations = $10,000 fine, 3 violations = $10,000 fine, 4 violations = $10,000 fine, 5...

It would be appreciated if someone could verify that this makes sense. By definition \bar{x} = \frac{\sum x_i}{n} So taking its expectation we get \bar{x} = \frac{1}{n} E[\sum x_i] Now, as we have a population of size N and a sample size of size n, we have {N\choose n} different samples and...

Hi All, I'm struggling to understand following problem. It says, Demand follows a triangular distribution. Minimum 500 Mode 6,000 Maximum 24,000 Expected demand is given as 10,167. To me, expected value should be the mode i.e. 6000. I'm struggling to understand the...

Hi All I'm looking for a metric that shows a close trend (good correlation) to the mean (expected value) of a distribution, so I can investigate the trend of that metric instead of mean when I don't have access to mean. Any suggestion? Thank you

Hi! First post here so cut me a bit of slack :) Hopefully an easy topic too (I'm new to stats). If I have some values for E(X) (e.g. 5min) and Var(X) (e.g. 2min^2) for a uniform distribution for say, the waiting time at a bank, how can I calculate, for example, the E(X) and Var(X) over a week...

I am interested in estimating E[g(h(X))] where... - X ~ Normal(mu,sigma) - h(.) = CDF of Standard Normal distribution - g(.) = inverse CDF of Beta distribution with known parameters alpha and beta Any suggestions as to how to proceed? Taylor approximation? Any help appreciated. Jesse

The problem is: Consider the experiment of tossing two dice. Let Y denote the absolute difference of the upturned faces. A) Find the mean and variance of Y. B) Find the expected value of 2/Y