If X is continuously and uniformly distributed between 1 and 5. What is the P(X<4)? of Select one: a. 0.75 b. 0.55 c. 0.65 d. None of these e. 0.80 CS Scanned with CamScanner

Q: Using the given data. Compute f"(1.4) at O(h2) using h=0.4. X у 1.0 2.9170 1.2 9.2005 1.4 20.5173…

A: Consider the given table, x 1.0 1.2 1.4 1.6 1.8 y 2.9170 9.2005 20.5173 38.0675 63.0511 The…

Q: x 2.6 4.1 3.3 4.5 2.6 3.2 3.4 y 5.0 10.0 11.2 10.0 7.9 3.9 5.5 verify that Σx = 23.7, Σx2 = 83.27,…

A: Given : x 2.6 4.1 3.3 4.5 2.6 3.2 3.4 y 5.0 10.0 11.2 10.0 7.9 3.9 5.5

Q: a. 24 T (¹7) r(5)r(7.25)

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Q: Assume X is normally distributed with a mean of 12 and a standard deviation of 2. Determine the…

A: Solution-: Given:μ=12,σ=2  We find x,  (c) P(x&lt;X&lt;12)=0.2 (d) P(-x&lt;X-12&lt;x)=0.95 (e)…

Q: a. Generate the 1000 revenues and retain the integer portion. b. Obtain a histogram for the data in…

A: We will generate 1000 revenues from an exponential distribution of parameter 1import numpy as np 2…

Q: The OLS residuals, eį, are defined as follows: a. Îi – Ôo – Ô₁ X₁. - b. yi-00-0₁ X₁. c. Yi - Yi. d.…

A: Ordinary least squares (OLS) regression is a statistical method of estimate the relationship between…

Q: a. Determine the marginal p.d.f.'s of X and Y. b. Are X and Y independent? c. Are the event (X 1/2}…

A: It is asked to find the marginal pdf's of X and Y. Marginal pdf of X. fx(x) = ∫0132y² dy=32∫01y²…

Q: Number of cups of coffee served at a restaurant. Select one: O a. Continuous O b. Discrete

A: We have to find that the number of cups of coffee served at a restaurant is discrete or continuous…

Q: For which value of x is p = (1,0, x) orthogonal to ā q = (10,3, –2 )? %3D 5.

A: Solution:- step:1      ∗vectors are  orthogonal if the dot product of the  two vector          is…

Q: 2x,0 < x <1 Let f(x) = 10, otherwise (note that X is continuous). a. Calculate E(X): b. Calculate…

A: The question is about to find expected value, variance using given p.d.f Given : f(x)= { 2x…

Q: The standard deviation of the y(t)=3 sin(20rtt) is: 1.0606. O 2.1213. O 1.6062 O 2.2123.

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Q: Let X1,...,Xn ∼ iid Pois(θ), and we wish to estimate φ = Pθ(X = 0) = e−θ. Consider Yi = I (Xi = 0).…

A: Given that  and

Q: Suppose that X is normally distributed with u = 10 ando 2. Find P(IX 10|S3)

A:

Q: a) Prove that if YE(A), then for all t and s, P{Y >t+sY>t} = P{Y > s}. (2.16) b) Prove that if Y is…

A: As asked, I have solved the question (b). Please find the solution below. Thank you.

Q: 3.6.14. Show that 1 1 + (r₁/r₂)W' where W has an F-distribution with parameters r₁ and r2, has a…

A:

Q: 00 dt

A: ∫0∞ e-t2dt

Q: In the fiqure below, How many measurements in a data set that subject to a random error and lies in…

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Q: Suppose that P(T)=0.51, P(B)=0.28, P(B\T)=0.18 and P(T or B) is closed to 0.444 O 0.16 O 0.6982 O…

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Q: Find Disjunctive Normal Form of following expressions. Show the complete Process. a. (pv-q) →q b.…

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Q: Evaluate. S2 (1+*)*dx=] (Type an exact answer.)

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Q: A dataset is collected, giving the values [1.2, -3 4.1]. Construct a RV y whose PDF has the same…

A: The Dirac-delta function is a mathematical construct which helps in simplifying computation which is…

Q: .8.3 Suppose X is uniformly distributed over the interval [0, 3], and Y = (X− 1)². Find the CDF,…

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Q: 2. In coherent radio communications, the phase difference between the transmitter and the receiver,…

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Q: 103 and o = 5. Determine the following Assume X is a normally distributed continuous variable with u…

A: Given Information:Mean, μ=103Standard Deviation, σ=5To find out Px≤88

Q: The following s a list of 6 measurements. 13, 18, 16, 7, 7, 12 Suppose that these 6. measurements…

A: According to the provided information, the list of measurements are: 13, 18, 16, 7, 7, 12

Q: 1) Assuming 11 degrees of freedom, find to.09(df). to.09(df) = 2) Assuming 15 degrees of freedom,…

A: here use t distribution table for getting t critical value

Q: 13.5 8.5 c13.5 | f(x) dæ = 4, f(x) da = 7, f(x) dx = 5. 11 Let %3D f(x) dx = 8.5 Find 8.5 4f(x) – 7…

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Q: The current in a semiconductor diode is often measured by the Shockley equation I = 10(eav 1) where…

A: Step 1:Step 2:

Q: 4. The Cov(xr, y,) between x and y for the following data : Σ-15 Σy= 36, Σxy 110, X; 7 = 5 is :

A:

Q: Suppose that the weight of an newborn fawn is Uniformly distributed between 2.5 and 3.7 kg. Suppose…

A: The random variable X is the weight of a newborn fawn It is uniformly distributed. X~U(a=2.5,b=3.7)…

Q: 3. Suppose a random variable X has pdf given by f(x) = |cos(x)1/4 for n/2 sx s 5n/2. Find the median…

A: To find median we use the formula, Integration|xM f(x)dx = 1/2 Where M is median

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!