Let X be the random variable with PMF: P(x) = k(]x – 2|+ 1), for x= -2, -1, 0, 1, 2 0, elsewhere (a) Find the value of k (b)Find the PMF of X (c) Find the mean, variance, and the standard deviation of X

Q: Let X be a normally distributed random variable with mean 600 and variance 10,000. Find two values A…

A: Given Information Mean µ = 600 Variance V(x) = 10000 Standard deviation is given by

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: Let X and Y be independent random variables with means ux, μy and variances o, oy. Find an…

A: Given:  Random variable x and y are independent with means ux, uy  , varience σ2(x) and σ2(y)  E(x)=…

Q: Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y…

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Q: X is a random variable with mean  μ  and variance  σ2  . The standard form of X is Z =( X — μ)/σ  .…

A: We want to find mean and variance for Z

Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: Let X be a random variable with a mean equal to 100 and a standard deviation equal to 15. Let…

A:

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. Find…

A: X follows a  normal distribution with , µ= -1 , σ= 1. Y follows a  normal distribution with , µ= 1 ,…

Q: Let X1 be a normal random variable with mean 2 and variance 3 and let X2 be a normal random variable…

A:

Q: The CDF F(x) of a random variable X is given by; F(x) = { 0, if x 3 } i) the mean and variance of…

A: Here,fx=dfxdx=dcx-14dx=4cx-13                                    ;1<x≤3   Now, find c using the…

Q: Let X have a mean of 132 and a variance of 32. Define Y=X² + 2X+1. Compute the (a) mean and (b)…

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Q: Suppose that f (x) = x / 8 for 3 < x < 5. Determine the mean and variance of x.

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Q: Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type…

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Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: b) Find the variance Var(X) of X.

A:

Q: Given f(x) = { (x2+1)/30; x = -2,-1,0,1,2  0; elsewhere ] Find the mean and variance of X.

A: X-2-1012f(x)

Q: Find the MGF of the binomial distribution ()ra- Use it to show that the mean is p and the variance…

A: Given that the pmf of the binomial distribution is P(X=x)=nxpx1-pn-x, x=0, 1, 2,..., n. We have to…

Q: Let X be a normally distributed random variable with mean 600 and variance 10,000. Find two values…

A: Given Information Mean µ = 600 Variance V(x) = 10000 Standard deviation is given by

Q: A random variable X has P(5<X<19) 2 0.75. Using Chebyshev's theorem, the mean and variance (H, o2)…

A: The mean will be the average of 5 and 19. So, mean= (5+19)/2=12

Q: Let X 1 be a normal random variable with mean 2 and variance 3 and let X 2 be a normal random…

A:

Q: continuous random variables Z is known to have an Erlang (2,1.3) type PDF. what is the variance of Z

A: Given that Z is a continuous random variable having a distribution Erlang with parameters (…

Q: f X is a random variable such that: E(X) = 6.2 and E(X2) = 62.5, then what is the standard deviation…

A: Given: X is a random variable. E(X)=6.2 E(X2)=62.5

Q: Let X be a random variable distributed as a Normal with mean 0 and variance 2 (i.e., X ~ N(0, 2)).…

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Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

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Q: Assume that you have a random variable X which is binomially distributed, and someone told you that…

A: Assume that you have a random variable X which is binomially distributed, andsomeone told you that…

Q: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…

A: The given pdf is shown below:

Q: A random variable X takes value 1 with probability and the value 2 with the remaining probability.…

A: The total probability of any probability distribution is always 1.

Q: The random variable X takes value O with probability, and value 1 with the remaining probability.…

A: We have given information, The random variable X takes value 0 with probability 13, and 1 with…

Q: The random variable Z has the probability distribution shown below If  E(Z) =4 2/3find the values…

A: Given Information: The probability distribution of the random variable Z is given as: z 2 3 5 7…

Q: The mean and standard deviation of a random variable x are 0 and 4 respectively. Find the mean and…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.