The Moment Generating Function (MGF) for a random variable X, mgfx(t) is given. Find the probability:

Q: Let X refer to the sum of two rolled die. Describe the probabilities of each outcome. If pX(x) is…

A: It is given that x denotes the sum of two rolled dies.

Q: Value x de X P (X = x) -4 0.14 -3 1 0.23 4 0.17 3.

A:

Q: Value x of X -1 1 2 3 5 P ( X = x) 0.29 0.14 0.14

A: The values of X are -1, 1,2,3, and 5  The table shows the probability distribution for the discrete…

Q: Let X~N(2,1), Y~N(-1,2). X and Y are independent. Find the probability distribution for Z=X - 2Y.

A: The probability density function of normal variable is given by, f(x)=1σ2πe-12x-μσ2 Given: X~N(2,1)…

Q: Fill in the P(x=x) values to give a legitimate probability distribution for th discrete random…

A:

Q: e P(X=x) va

A: Given a table Value x of X P(X=x) -5 0.21 -1 0.13 1 0.12 2 ? 5 ?

Q: Find the expected value for the random variable: 1 2 P(X) 0.24 0.27 0.21 0.28

A: Given the probability distribution table: X 1 2 3 5 P(X) 0.24 0.27 0.21 0.28 Expected…

Q: The wait time for your local pizzeria to deliver food is normally distributed with µ = 35 minutes…

A:

Q: Find two lines of regressions from the following Data:  Age of husband : 25, 21, 22.5, 26.3, 35.7,…

A: It is required to find the two lines of regression, make the predictions, and obtain the correlation…

Q: Complete this PDF and find the expected value of X:

A: The P(x) for X = 2 is calculated as follows: PX=2=1-0.3+0.2+0.4               =1-0.9…

Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

A: Solution : Value x of X Probability -3 0.27 3 0.27 4 0.30 5 0.19 6 0.26 Explanation:…

Q: Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random…

A: Given that,Value of X     P(X=x)-2                   x-1                   x3…

Q: (d) Find the probability that no tires have low air pressu The probability that no tires have low…

A:

Q: Calculate the expected value E(X) of the given random variable X. X is the lower number when two…

A: Two dices are rolled.

Q: find the probability that a random chosen point i in the figure lies in the shaded region.

A: The entire region is a equilateral triangle of side length=a=10 inSo the area of the…

Q: According to rainfall data collected by a laboratory during storm events, the precipitation level in…

A: Solution

Q: x is a random variable with the probability function: f(x) = x/10 for x = 1, 2,3 or 4. The expected…

A: Given that  x is a random variable with the probability function: f(x) = x/10 for x = 1, 2,3 or 4.…

Q: Suppose we ask a basketball player to shoot 4 free throws. Let the random variable of interest x…

A:

Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

A:

Q: X is a discrete variable with the probability distribution B(18, 0.35) Determine the value of Fx(4).

A: given data : binomial distribution  X~B(18,0.35) n = 18 p = 0.35 FX(4) = ?

Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

A: As the sum of all probabilities for a probability distribution results equal to 1, that is ∑P(X = x)…

Q: Value x de X P(X = x) 0.30 2 0.26 4 5 6 0.10 1.

A: We have given that,        X       :-    1        2         3     4       5 P(X= x) :-   0.30…

Q: Fill in the P(X=x) values to give a legitimate Value x of X P(X = x) -2 0.28 4 0.21 6. 0.16 1.

A: Introduction: The random variable of interest here is X, which takes the values, x = -2, 1, 4, 5,…

Q: If n = 19, ¯xx¯ = 34, and s = 20, construct a confidence interval at a 95% confidence level. Assume…

A:

Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

A: It is given that a legitimate probability distribution for the discrete random variable X whose…

Q: An average of 4.55 customers comes to Columbia Savings and Loan every half hour. Find the…

A: given data,An average of 4.55 customers comes to Columbia Savings and Loan every half hour.here…

Q: USE 3 DECIMAL A financial analyst wants to understand the preference of the people investment…

A: Null and alternative hypotheses : Where, p1 is the proportion of people in 2010 who prefer to…

Q: P(x = x) Value x of X 0.11 3 4. 0.10 6. 0.23

A:

Q: Fill in the P (X=x) values to give a legitimate probability distribution for the discrete random…

A: Given probability density is : Value of x of X P(X=x) 2 0.25 3 0.25 4 ? 5 0.22 6 ?…

Q: P(X = x) Value x of X 0.27 0.22 0.17 6. 2. 3.

A:

Q: Compute​ P(X) using the binomial probability formula. Then determine whether the normal distribution…

A: The binomial probability formula is, PX=x=nxpx1-pn-x In the formula, n denotes the number of trails,…

Q: Fill in the P (X=x) values to give a legitimate probability distribution for the discrete random…

A: Let X be a discrete random variables

Q: 4 f(x) = OTHERWİSE 0, -12112

A: EX=∫-20x.fxdx+∫02x.fxdx=∫-20x12+x4dx+∫02x12-x4dx=∫-20x2+x24dx+∫02x2-x24dx=12∫-20xdx+14∫-20x2dx+12∫02…

Q: Value x of X P(x =x) -6 -5 -4 0.12 -3 0.17 3. 0.15

A:

Q: Using 2 independent CRV A and B with probability distribution fa(a) and f;(b) below, find the…

A:

Q: Fill in the P (X=x) values to give a legitimate probability distribution for the discrete random…

A: ?, 0.30, 0.22, 0.24, ?

Q: The probability of a Type Il error is represented by the symbol B (beta). True O False

A: In this case, we need to identify the given statement is true or false.

Q: Find P(XS3) if the cumulative distribution function for the random variable X is: 0, x<-1, 0.25,…

A: From the given information, let X be a random variable having the cumulative distribution function…

Q: the P(X=x) values to give a legitimate probability distribution for the discrete random variable X,…

A:

Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

A: Given The P(X=x) values to give a legitimate probability distribution for the discrete random…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!