A surface has infinite parallel lines at distance d from adjacent lines. We have a needle of length I which we throw randomly on the surface. What is the probability that the needle intersects a line? Assume l < d.

Q: Suppose that 2 balls are randomly selected from an urn containing 3 red, 4 blue, and 5 white balls.…

A: Given: 3 red, 4 blue, and 5 white balls X= number of red balls Y= number of white balls n = 2

Q: (d) The probability that a randomly selected hybrid gets less than 45 miles per gallon is (Round to…

A: X follows a Normal distribution with mean = 57 and S.D = 3.5 Then z=(x-mean)/SD = (x-57)/3.5…

Q: From the Gaussian error curve, what is the probability that a result from population lies between -o…

A: We want to find P(mu-sigma&lt;X&lt;mu-3sigma)= ?

Q: let flx)=, V2 Cunsrder y=x? Find the probability densily funchon of Y

A:

Q: Suppose X has a normal distribtution N(2,1), then E(X)= Var(X)=

A: Let  X has a normal distribution X~N(µ=2, σ2=1)Then the value of Mean =E(X)=µ=2Variance=Var(X)=σ2=1…

Q: Find the value of c guaranteed by the Mean Value Theorem of intergrals... Given (x) = on [1,e?]

A:

Q: A computer disk storage device has ten concentric tracks,numbered 1, 2,…, 10 from outermost to…

A: The conditional probability that the arm is on track i is, p(X=j)=∑i=110p(X=j|arm on i).p(arm on…

Q: Let the r.v. X~N(0,0²)what is the probability that the random Intreval include the point o . What is…

A: Given : X~N0 , σ2

Q: Suppose that X has a hypergeometric distribution with N = 1200, k = 800 and n=300. Find the…

A: Solution

Q: n points are scattered at random independentlly of oneanother inside a sphere of r. • What will be…

A: Let A be the sphere of radius R and B be the sphere of radius r. Volume of sphere A is: 4πR33 Volume…

Q: A die is loaded in such a way that the probability of the face with j dots turning up is…

A: Given A die is loaded in such a way that the probability of the face with j dots turning up is…

Q: N points are scattered at random independently of one another inside a sphere of radius R. •  What…

A: Answer for sub question 1: Let A be the sphere of radius R and B be the sphere of radius r. Volume…

Q: The joint distribution of X and Y is given by fXY (x) = 4x y e- (r* + y*), x2 0, y 2 0 Show that and…

A:

Q: The length of a phone call is assumed to be uniformly distributed over the interval (0, 0 + 1),

A: Given information: Given that the random variable X follows uniform distribution over the interval…

Q: N points are scattered at random independently of one another inside a sphere of radius R. • What is…

A: Let, v(r) be the volume of a sphere of radius r. For a single point in the sphere of radius R with…

Q: A surveyor wishes to lay out a square region with each sidehaving length L. However, because of a…

A: The north–south sides both have length X. The east–west sides both have length Y.  X and Y are…

Q: The probability of observing a head and an ODD # on the surface of the die.

A: Here the two events are independent   For flipping a coin : There are two outcomes : Head , Tail…

Q: The amount of time, in minutes, that a person must waitfor a bus is uniformly distributed bet ween…

A:

Q: Suppose, the walking speed of an elderly is no more than 6 km per hour. The walking speed, Y, in km…

A:

Q: Will you show me step by step how to answer this, please?

A: Given Datan = 3p = 0.8X = 2Applying Binomial theoremProbability of x success out of n trial is given…

Q: ous Tan dom valnable A Lion TunC 0, for x < -2, 3 1 + 4x - 32 2 for – 2 <x < 2, 3 F(x) 1, for x 2 2.…

A: Solution

Q: If repeated random samples of size 40 are taken from an infinite population, the distribution of…

A: Solution-:  If repeated random samples of size 40 are taken from an infinite population, the…

Q: What do the functions Y LY, Y look like? Are there any maximum or minimum probability at any…

A: By the functions Y1,1 , Y1,0 , Y1,-1. Y1,1=-38πsinθeiφ The probability density is:…

Q: Consider that a researcher is attempting to reduce the expected distance between M and µ as much as…

A: The size of the sample plays a very important role when it comes to sampling distribution. Big…

Q: A unit length, thin rod breaks in two places, each break independently uniformly distributed on [0,…

A: Rod : unit length Break in two places independently We have to help to understand the answer which…

Q: IF X and Y ae random Weriables whose joint denjity funchion f is given as 6thernise Compute the…

A:

Q: A humane society claims that less than 72% of households in a certain country own a pet. In a random…

A: a) Given claim of the problem is less than 72% of households in a certain country own a pet.…

Q: Y Two points are taken at random on a given straight line of length 2 units. Prove that the…

A:

Q: An amateur statistics practitioner proudly shows you the graph above (Fig. 1) and insists that it is…

A: c) From that part a, the value of K is 1/8. From the given graph, the probability density of X is,…

Q: How could the central limit theorem be used to gauge the probable size of the error of the estimate…

A: Given that A=0.2             P(A^-A&lt;0.01)≈0.99

Q: If two points are selected on a straight line of length a units at random, find the probability that…

A: first Consider one of the ends of the line segment as origin. Let the two points chosen be at…

Q: A metal rod of length L and a sphere of radius R are to be joined to form a small automobile part. L…

A: EL=2    VR=0.052     ER=0.5     VR=0.052     VL=0.12   Since L and R are normally…

Q: From the Gaussian error curve, what is the probability that a result From population lies between +o…

A: Given that Area under the curve for ±σ is 68.3% and for ±2σ is 95.4%.

Q: 2. An agronomist want to take soil sample from a circular patch of ground with radius 9 meters.…

A:

Q: 26. A stone is thrown into a circular pond of radius 1 meter. Suppose the stone falls uniformly at…

A: Given, A stone is thrown into circular pond of radius, r = 1 meter Stone falls uniformly at random…

Q: The coefficient of thermal expansion, of steel, is given at discrete values of temperature in Table…

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Q: Let Y and Y, be independent and uniformly distributed over the interval (0, 1). Find the probability…

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Q: A research center claims that 26% of adults in a certain country would travel into space on a…

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Q: ) Suppose the diameter at breast height (in.) of trees of a certain type is normally distributed…

A: Given Mean =8.8 Standard deviation=2.8

Q: The first four moments about the mean, are 0, 8, -144 and 14817 calculate the skewness based on…

A: Given information μ1=0 μ2=8 μ3=-144 μ4=14817

Q: Let C be a unit circle centered at origin. Point P1 is chosen randomly from the circumference of C.…

A: Here it is assumed that the first  point  depicting the point on the circumference of circle be…

Q: A hexagonal cell within a seven-cell system has a radius of 1.425 km. A total of 119 channels are…

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Q: Find the nth moment of uniform random vari- able and hence its mean.

A:

Q: 23. Through a point B on the y-axis whose ordinate is possible and equal to a, a straight line is…

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Q: Find kurtosis by using quartile deviation(formula given in picture).

A:

Q: 040. If the probability is 0.05 that a certain wide-flange column will fill under a given axial…

A: Given P=0.05 q=0.95 n=16

Q: If the probability density of a random variable is given by |С ехр(-x/4), 0<x<1 fx (x) otherwise…

A: