2. For the Cauchy distribution: 1 C(x; γ) %3D 2 (X – Xo - TY |1 + a. Derive the mean of the distribution b. Write (without derivation) the characteristic function for the distribution. What are the values of its derivatives at 0?

Q: Find the mean value of f(x) = |x| on the interval [-1, 4]. %3D

A: Given that: f(x)=|x| in [-1, 4]

Q: Answer the following questions: f(x) 1871 0.0 0.2 0.4 0.6 0.8 1.0 10 T T 0 5 10 15 20 25 30 a. The…

A: A gamma distribution having two parameters with α and β. MDifferent Formula of the  gamma…

Q: Find the mean value of the function y = 4cos x on the interval 0,

A:

Q: 03- Calculate Median and Mode from the following data: Class 20-24 25-29 30-34 35-39 40-44 45-49…

A:

Q: The joint and marginal pmf's for X = automobile policy deductible amount and Y = homeowner policy…

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

Q: Find the mean value of y = x² - 7 over the range -2 < x < 2, and enter your answer as a decimal in…

A:

Q: Let the r.v X~P(4). Then the mean and variance are? Find Pr(X>5)?

A:

Q: Let X - T(28). Find P40(x) (50th percentile of X)

A: The (100p)th percentile is the value xp of the distribution such that (100p)% of the distribution…

Q: The length of eels (in cm) in a river may be assumed to be normally distributed with a mean of μ=46…

A:

Q: For a highway, the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X is…

A: It was stated that the car's speed has a uniform distribution [50,90]. Cars are stopped if speed X…

Q: Suppose that the function f(x) 20.25 average molecular speed for this distribution? Write your…

A: Solution is given below:

Q: at x=3.

A:

Q: Let X - T(25). Find P30(X) (30th percentile of X)

A: Solution: From the given information, X follows T distribution with degrees of freedom 25.

Q: For a​ t-curve with df=9​, use a​ t-distribution table to find the​ t-value t0.025.…

A: From the provided information, Degree of freedom (df) = 9 The level of significance (α) = 0.025

Q: Find the p values as a range (to 3 decimals places) (a) right tailed test  t=1.457, d.f. =14.…

A: From given  t=1.457 d.f. = 14

Q: 1.Given t distribution, find values of t(5)0.2 2.explain the relations between them with Z0.2

A: Given, t-score =  0.2 dgrees of freedom = 5 z-score = 0.2       To find, a. find the value for…

Q: P( z>1.31) =

A: The value of Pz&gt;1.31 is, Pz&gt;1.31=1-Pz&lt;1.31 The probability of z less than 1.31 can be…

Q: A farmer in Indiana wants to examine the relation between the number of very hot days temperature…

A: Hi, thanks for posting the question. Since there are more than three sub parts posted in the…

Q: oy be regarded as a RV having an Erlang distribution with A = 1 and k = n In. If the sales cost is…

A:

Q: For the following set of discrete data: 1.0 ind: X Y 2- 1.729 1.5 1.691 2.0 1.505 d²y at (x = 2.0)…

A: x 1.0 1.5 2.0 2.5 3.0 Y=f(x) 1.729 1.691 1.505 1.416 1.311 Estimate f′′(2.0). Central…

Q: I. The following table gives the distribution of a r.v. X ,where a and B are constants, -2 2 P(X=x)…

A: Note: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: The following graph is a standard curve based on the concentrations (in ppm) of the standards…

A: Given the instrument response = 0.8 We will draw lines parallel to the x-axis (as shown in below…

Q: Che following table relates to the profits and losses of 100 firms. Calculate the average profits…

A:

Q: What does this formula compute? E (Y-Y')² N Oest Select one: O a. Variance of Y O b. Variance of the…

A: Given Information: Formula: σest=∑iY-Y'2N (a), (b) are the variances of Y and slope. Variance…

Q: Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi)…

A: As there are multiple question, we will answer the first question according to Bartleby policy.…

Q: 3. Let X~~ Pois (4). Find the distribution of Y = √X. 2

A: the distribution of y = √x when x follows a Poisson distribution with parameter λ = 4, we need to…

Q: Let X-T(4) and Y-x2 (4). The following plot depicts the cumulative distribution functions of X and…

A: Statement is true.

Q: Write an absolute value function f(t) to describe an individual variance from normal body…

A: Write an absolute value function f(t) to describe an individual variance from normal body…

Q: Assume x is exponentially distributed with a mean of 4. Find: a.P(X=2) b.P(X=2) d.P(2 < X < 4)

A: As per guidelines we are allowed to solve maximum of 3 subparts, Please repost the question if you…

Q: Suppose that x has an exponential distribution with θ =1.5. Find P(x > 1

A: The probability distribution is given by: f(x) =1.5e(-1.5x)    for x&gt;0

Q: 3. a. (0.25, 0.75) Evaluate using Beta Function:

A:

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!