X is a normal random variable with mean 0 and standard deviation 1. Y is uniformly distributed between and 0, for X + 0. What is the conditional expectation of X given that Y = 4? [Hint: you will need to

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A: According to bartleby policy i have solved first three subparts of this question. I hope it will…

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A: Here alpha = 3 , beta = 10 Mean = 3×10 = 30 Standard deviation = 10 √3 = 17.32

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A:

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A: Note: Hi there! Thank you for posting the question. As there are multiple sub parts, according to…

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Q: The table on the last page displays the cdf for continuous random variable X, which has a mean of 1…

A: We know, the median divides the data into two equal parts, therefore, If PX≤x=PX≥x=0.5, then x is…

Q: Use 68-95-99.7rule and note that Z ~ N(0, 1).

A: Here it is given that, Mean (μ) = 5 Standard Deviation (σ) = 10 Using 68-95-99.7 rule, we have, 68%…

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A:

Q: In the probability distribution to the right, the random variable X represents the number of…

A: Solution 0 0.269 0 0 0 1 0.571 0.571 1 0.571 2 0.123 0.246 4 0.492 3 0.031 0.093 9…

Q: A discrete random variable X has its probability mass function given by this histogram. 0.45/ 0.4…

A:

Q: Compute the mean and the Standard deviation of the probability distribution table of :   X…

A: Note: Thank you for the question. Since multiple questions are posted, according to our policy, we…

Q: We have provided the parameter of a Poisson random variable, X. a. determine the required…

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Q: Let X be a random variable with the following probability distribution: X -4 3 5 f(x) 0.3 0.2 0.5…

A: Given,E(X)=∑X.f(X)

Q: P(x) 0.645 1. 0.297 0.052 0.005 0.001 0.000 2345

A: We have to use following formulae , Standard deviation : σ = ∑( x - μ)2p(x) Where , μ is mean μ =…

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A: Given:  X 2 3 4 5 6 FX 0.01 0.25 0.4 0.3 0.04   Formula: Meanμ =∑X PX Variancex=∑i=1nX-μ2…

Q: Let X be a discrete random variable with Poisson distribution, and with parameter 64. What is the…

A:

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

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A: Given information: X~N+μ, σ Y~N-μ, σ

Q: y -2 1 4 -1 0.2 0.1 0.2 3 0.1 0.2 0.1 0.1

A: We need to find P(X=5)

Q: 1. Let X be a Gaussian random variable with mean 6 and standard deviation o? = 10. Find (a) P(X> 6)…

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Q: The random variable X, representing the number of errors per 100 lines of software code, has the…

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Q: Let X be a random variable with the following probability distribution: X -2 3 5 f(x) 0.5 0.2 0.3…

A: population mean : μ = E(x)

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Q: Calculate the standard deviation o of X for the probability distribution. (Round your answer to two…

A: From the given information, X -5 -1 0 2 5 10   P(X=x) 0.1 0.2 0.3 0.1 0.3 0   XP(X=x) -0.5…

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Q: Calculate the standard deviation o of X for the probability distribution. (Round your answer to two…

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Q: Consider the following probability distribution. X 1 3 4 6 P(x) 0.02 0.05 0.17 0.35 0.22 0.17 0.02…

A: Formula Used: For expected value of x. E(x) = ∑xP(x) For standard deviation of x. SD(x) = VAR(x) For…

Q: places.) x 0 1 2 3 P(X = x) 0.4 0.3 0.1 0.2 ? =

A: Given information- We have given the probability distribution for X. The given observations and…

Q: The following is a probability distribution for a discrete random variable X. 0 1 P (x) 0.2 0.8 The…

A: Given,

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Q: The following is a probability distribution for a discrete random variable X. P (x) 0.4 0.6 The…

A: From the provided information, x 0 1 P(x) 0.4 0.6

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A: Binomial distribution: The binomial distribution gives the probability of number of successes out of…

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Q: On the midnight shift, the number of patients with head trauma in an emergency room has the…

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Q: Find the standard deviation of X. O 0.86 O 0.92 O 0.98 O 0.79

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A: The probability of x less than 49 is, Thus, the probability of x less than 49 is 0.9641.

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A:

Q: a normal distribution has a mean of u=60 with o=15.  if one score is randomly selected from the…

A: let "x" be the score.

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A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks   For the…

Q: Let X be a random variable with the following probability distribution. Calculate the following…

A: X 4 5 6 7 8 9 P(X=x) 0.60 0.10 0.05 0.15 0.05 0.05

Q: Let x be a random variable with the following probability distribution 1 3 P(x) 0.3 k 0.1 0.2 Find…

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Q: Find the probabilities for each using the standard normal distribution. P( z> 0.56)

A: We have to find P(z > 0.56)

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!