Can you help: Suppose X ∼ Norm(0, 1). Find Var(X). (Hint: we know that 1 √ 2π R ∞ −∞ e −x 2/2dx = 1.)

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A:

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Q: Question 3 * We candomly select one ball from Containing 12 red and 10 blue balls. Find the…

A: Total balls = 12 + 10 = 22Red balls = 12, Blue balls = 10

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A: According to guidline we are supposed to solve first 3 subpart only,rest can be resubmittedThanku

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Q: Size Cumlative weight (%) 2 2 3 10 5 40 7 70 10 92 25 99.9 Determine if this distribution is log…

A: SizeCumulative weight (%)2231054077010922599.9

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A: sample size(n)=75Mean()=223standard deviation()=5.9

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A: n=5008x=760

Q: Suppose X ∼ Norm(0, 1). Find Var(X).

A: Suppose The PDF of the standard normal variate is written as follows:

Q: Help please: Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1).…

A: Pdf of nth order Statistic is f(x(n))=n(F(x))n−1f(x)

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Q: A manufacturer knows that their items have a normally distributed lifespan, with a mean of 4.6…

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Q: 2. Let X be a continuous random variable with probability density function (pdf) [3x² 0<x<1…

A: f(x)=3x2.       0&lt;x&lt;1 0.               OtherwiseWe have to find the probability density…

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A: Take  to be the state of the machine in the morning of day  when .The states of the given Markov…

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A: Given that  be the Markov chain on state space  with transition matrix:

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A: From the provided information,

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A: Given,

Q: me please: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let

A: We have given that X1, X2 ∼ Unif(0, 1)

Q: Consider the following cumulative distribution function for the discrete random variable W. W 2

A: Given that  w1234P(W&lt;=w)0.30.440.721

Q: Find the z-scores for which 80% of the distribution's area lies between -z and z. Click to view page…

A: From the provided information,80% of the distribution's area lies between -z and z.

Q: The weekly repair cost Y for a machine has a probability density function given by 3(1-y)², 0<y < 1,…

A: Given that

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A: The proportion of a population under the age of 18 is known to equal 0.42.

Q: Two-dimensional random variables (X, Y) ~ f(x, y) = 1, 0<x<1,0 <y < 2x {1 otherwise fx (x) (1) Find…

A: f(x,y)= 1 ; 0&lt; x&lt;1, 0&lt; y&lt;2x

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A: It seems you have submitted 3 different questions, as per the guidelines I can solve the first one.…

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A: The mean arrival rate is cars per hour.

Q: 2. Let X₁, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix /1/2 1/2 0 0…

A: Given that  be the Markov chain on state space  with transition matrix:

Q: 4.144 Consider a random variable Y with density function given by f(y)=ke-²/2 a Find k. b Find the…

A: a) The integral of the density function over its entire range must equal 1 since the total…

Q: If X is a discrete uniform random variable ranging from 1 to 8, find P(X > 1).  a. 0.7500 b. 0.8750…

A: It is given that X is a discrete uniform random variable ranging from 1 to 8.

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A: The pdf of the Weibull distribution is: thethe values of the parameters are .

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A: It is given that x = 556n = 914Confidence level = 95%

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Q: Suppose a discrete random variable X has range {-1, 0, 1, 2, 3} and cumulative distribution function…

A: The  is the discrete random variable with a range of values .The cumulative distribution function…

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Q: estaurant in Ohio, the number of minutes that diners spend at the table has a major impact on the…

A: X~N( μ , ?)μ=89 , ?=17Z-score =( x - μ )/?

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Q: Consider the following discrete probability mass function. X P(X=x) 3 0.25 1 0.30 Find P(X≥ 1).…

A: The provided information is as follows:The probability mass function is given as  310.250.30.45

Q: Suppose you roll a die until the first time you obtain an even number. Let X1​ be the total number…

A: Roll a die until the first time you obtain an even number.X1​ is the total number of times you roll…

Q: 6. Suppose that P(E)=0.61, P(F) = 0.43, and P(EF) = 0.27. Find the following:

A: 6) Given,P(E) = 0.61P(F) = 0.43And 0.27Using formula,

Q: 5) The width of bolts of fabric is normally distributed with mean 950 mm and standard deviation 10…

A: Mean() = 950 mmStandard deviation() = 10

Q: There are 8 balls of which 2 are white and 6 red. For the first time, 2 balls are taken from the…

A: Total balls = 8 White balls = 2 Red balls = 6 First time : 2 balls are taken from the bag Than 2…

Q: Problem 3 A total of 36 members of a club play tennis, 28 play squash, and 18 play badminton.…

A: Let's define the following sets:T = members who play tennisS = members who play squashB = members…

Q: Consider the accompanying data on plant growth after the application of different types of growth…

A: I used R software for calculations.H0: Ha: at least two  are unequal. (Option 4th)Alpha = 0.05Test…