Let the random variable Z = k+ mW. Then, Pz = mµw- %3D

Q: Given the normally distributed random variable X with o = 10 and P(X < 40) = .0080, find u.

A: Note: Please repost other question as i can answer only 1 question as per my policy.   28) Given…

Q: If Z denotes the standard normal random variable , then  P( -.58 &lt; Z &lt; .23) ?

A: The z-score is the number of standard deviations by which an event is occurring is over the mean…

Q: If Z is a random variable having the standard normaldistribution, find the respective values z1, z2,…

A:

Q: a) Calculate the covariance of Y₁ and Y₂. b) Are Y₁ and Y₂ independent? Are two uncorrelated random…

A: The given table:   Y1 -1 0 1 Y2 -1 1/16 3/16 1/16 0 3/16 0 3/16 1 1/16 3/16 1/16…

Q: If z is a standard distributed random variable, what is the probability of P(z<2.04)? a) 0.9793 b)…

A: It was stated that Z is a standard normal variable. Need to find the probability of P(Z&lt;2.04).

Q: |Consider random variables Y,, Y2, ...,Yn, each with distribution N(µ, o²). In addition, Corr(Y, Y,)…

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Q: Be A and B independent random variables with variances o2 and o3, respectively. Being D = A + B and…

A:

Q: For the random variable X, E(X+1) = 3 , E(X- +X)= 9 then the value of Var(X) is 10 3 0 2 0 50

A: Given, E(X+1)=3 Then E(X)+1=3          E(X) =2 and E(X2+X)=9       E(X2)+E(X)=9       E(X2)+2=9…

Q: For a uniform random variable X - U(20, 26), find x0.6: (Round the answer to 4 decimal places) X0.6

A: It is given that, X~U(20,26) f(x) =1/(26-20) = 1/6 ; 20&lt;x&lt;26 We have to find x0.6 i.e. 60th…

Q: Which of the following are the values of the random variable? Ax- (1, 2, 3, 4, 5, 6, 7, 8, 9, 10} B…

A: Random variables: A variate may be a numerical illustration of an applied mathematics experiment's…

Q: Let X be a binomial random variable with mean u = 2.2 and %3D variance o = 1,76, find %3D a) Write…

A:

Q: Find a value of the standard normal random variable z, call a. P(zszo)=0.0283 b. P(-Zo szsz0)= 0.90…

A: Givena)P(z≤z0)=0.0283

Q: |If the expected value of the random variable X is 1/3. Find the values A and B.

A:

Q: If X is a normal random variable with parameters µ = 3 and o² = 9, find P(2 0). с. P(|X – 3| > 6).

A:

Q: Which is a discrete random variable? X= ^ n Welght of the microprocessor Inside your computer" Y =…

A: A variable can either be continuous or discrete.

Q: Z is a standard normal random variable. The P(-1.96 Z -1.4) equals

A:

Q: The Proportion of during the Month whith Stationary supply Sold beta random Variable a d = 4 and B=2…

A: Given: X~Beta(α=4,β=2)   Formula Used: The probability density function of beta distribution is…

Q: Let the random variable Y = a + bX. Then uY=a+b-ux

A:

Q: IF the variance of the discrete random variable X =36 * (2 Points) and if E (X²) = 100 , then E (X)…

A: We have to find E(x)..

Q: z is a standard normal random variable. The P2> 2.41) equals 0.0778 0.1075 O 0.9222 O 0.0080

A: The P(Z ≥ 2.41) equals is obtained below: From the given information the value of z-score is 2.41.…

Q: If the random variable ?takes the values 1, 2, 3, 4 such that 3P(X=1)= 4P(X=2 )= P(X=3) = 5P(X=4).…

A: It is given that, 3P(X=1)= 4P(X=2 )= P(X=3) = 5P(X=4)

Q: Let xbe a Bernoalli random variable with mean of 0.6. Find the var(2x) اختر احدى الدجابات None 0.9…

A: GivenLet X be a Bernoalli (p=0.6)

Q: For the standard normal random variable z, find P(z ≤ 0.57). Select one: A. 0.2877 B. 0.7157 C.…

A: Draw the normal curve and shade the area to the left of z=0.57.

Q: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2…

A: For a random variable X , suppose that E[X] = 3 and Var(X) = 4. Then (a) E[(5+X)^2]=   (b) Var (2 +…

Q: Which is a discrete random variable?   Z = "the weight of newborn African elephants"   X = "the…

A: The discrete random variable is:-

Q: Suppose a discrete random variable X takes only three values 0, 2 and 3. If P(0)=0.5, P(2)=0.2 and…

A: For a Discrete Random Variable X where X takes only three values that is 0,2 and 3 P(0)=0.5 ,…

Q: w. Determine if the random variables are statistically independent considering f (2, 1).

A: here given ,  joint distribution of x and y  two variables are statistically independent when f(x,y)…

Q: Let the random variable Y = a + bX. Then oy = |b| Ox.

A: False

Q: If z is a standard normal random variable, then P(0.20 <z< 1.47) is: .3305 .3499 .1844 .5279

A: The objective is to find the      Here, z is a standard normal random variable.

Q: In the linear model, R2 is: OA. a regular random variable. OB. an observable fixed number.

A: The regression analysis is a statistical procedure that allow us to find the linear association…

Q: Which of the following is a random variable? (choose all that apply) (a) p-value (b) х? (c) B1 (d) ŷ…

A: A random variable is a numerical description of an outcome of a statistical experiment. A random…

Q: Given z is the standard normal random variable, find c > 0 such that P(-c<z < c) = 0.135

A: given z is the standard normal random variable. z~N(0,1) find c=? s.t.  P(-c&lt;z&lt;c)=0.135    ,…

Q: The PDF of random variable W is c(w + 5), -5 <w < 7 fw (w) %| 0, otherwise

A: Given,f(w)=c(w+5);  -5≤w≤70;  otherwise

Q: Consider the three normal random variables Y Ν(μ-0,σ?4) , Y , Ν (μ Y3 ~ N(µ = -3, o² = 3). Find the…

A:

Q: Suppose that the joint probability for random variables X and Y defined by 01 28 28 28 21 3. 28 ZH…

A: Given: The joint probability for the random variable X and Y is given as:   y=0 y=1 y=2 f(x)…

Q: For a random variable X ~ Exp(2), find P(X < 1) and E[X].

A: Given: λ=2

Q: What is the Variance of a negative binomial random variable with parameters p= 0.35 and r=5? Select…

A:

Q: Let the random variable Y = a + bX. Then, Hy = bµx. %3D

A: Given equation Y=a+bX  E(Y)=a+bE(X)

Q: E[(1 – p)*] = (1 – p?y: %3D

A: Let a random experiment be performed repeatedly, each repetition is called a trial. let the…

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 probability distribution of the random variable X is: 4 6 0.3 0.4 2 f (x) 0.1 0.2 The variance…

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Q: The random variable X is related to e2. Find P(X>0.4).

A: It is given that the, The random variable X is related to e2 i.e. X ~ exp(2). We have to find P(X…

Q: Assume that Z is the standard normal random variable. (a) Find P(Z -0.59) (c) Find P(0.21 < Z <…

A: Policy: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Which of the following is a random variable? (choose all that apply) (a) p-value (b) x2 (c) B1 (d) ŷ…

A: Since, p-value having the nonlinear relation to the actual deviation from the mean. Therefore, the…

Q: Determine the distribution of the random variable X and sketch its graph. for x € (-00, -1) for r€…

A: We want to find random variable and sketch the graph.

Q: Let μ and σ2 denote the mean and variance of a random variable X. Determine: (a) E[(X −μ)/σ] (b)…

A: Let μ and σ 2 denote the mean and variance of a random variable X

Q: Suppose X is a normal random variable with u = 500 and o = 75. Find the value of: а. Р(Х 350) c.…

A: We are given that X is a normal random variable with μ = 500 and σ = 75.We have to find the value of…

Q: What is the sd of a random variable X with MGF 1 V(1-2t)

A: Mgf of chi square with n degree of freedom  Mx(t)=(1-2t)^(-n/2)

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!