Please show step by step explanations. Thank you. Given a random continuous variable X with some function f(x) where −∞≤x≤∞ what is the probability distribution function of X?

Q: The discrete probability distribution is given by. What is the mean of the probability distribution?…

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Q: Value x de X P (X = x) -4 0.14 -3 1 0.23 4 0.17 3.

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Q: A probability distribution function is given by  f(x)=7x−1100,x ∈{1,2,3,4,5}f(x)=7x-1100,x…

A: X f(x) 1 7-1100 = -1093 2 14-1100=-1086 3 21-1100=-1065 4 28-1100=-1037 5 35-1100=-1002

Q: P(x) A sociologist randomly selects single adults for different groups of three, and the random…

A: Solution: The probability distribution is  x P(x) x2 x*P(x) x2×P(x) 0 0.094 0 0 0 1 0.333 1…

Q: X P(x) 0 0.034 1 0.152 Five males with an X-linked genetic disorder have one child each. The random…

A: μ=Mean=E(X) E(x)=∑xP(X=x)

Q: Part D. Does the function f(r) = ()p" for a = 1,2 describe a finite probability distribution on the…

A: We have been given the function f(x) as follows, We need to check whether the function f(x)…

Q: Let X represent the time it takes from when someone enters the line for a roller coaster until they…

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Q: The discrete probability distribution is given by. What is the variance of the probability…

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Q: Use the table for the probability distribution to find the condition probability of X = 1 given that…

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Q: The number of cars per household in a certain neigborhood varies from 1 to 6. The probability…

A: From the provided information,The probability distribution table is as…

Q: Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd…

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Q: The table shows the number of car accidents per day and their corresponding probabilities. Find the…

A: 1)Given data is No. of accidents (x) 0 1 2 3 4 Probability P(x) 0.35 0.25 0.20 0.1 0.1

Q: The plot to the right shows the probability function of a random variable Z. Estimate the needed…

A: For the given plot Find P ( z >=3 or z =-1 ) = ? P ( z >=3 ) +P(  z =-1 ) = P( z = 3 ) + P( Z…

Q: If the probability distribution for a discrete random variable X is given by the following piecewise…

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Q: The table shows the probability distribution of the number of days (x) to complete a construction…

A: Solution-: Let, X- be the number of days We have, x f(x) 1 0.104 2 - 3 0.312 4 0.24 5…

Q: Conditional probability distribution Y given that X = 0.5 %D y f(x, y) -1.0 -2 1/3 -0.5 -1 1/6 0.5 1…

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Q: Conditional probability distribution Y given that X = 0.5 y f(x, y) -1.0 -2 1/3 -0.5 -1 1/6 0.5 1…

A: Solution is given below

Q: Find the distribution function which corresponds to the probability distribution defined by f (x) =…

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Q: 4. A discrete random variable X is known to have the following probability distribution function: x…

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Q: Find the probability distribution for the number of jazz CDs when 5 CDs are selected at random from…

A: There is 7 jazz CDs, 5 classical CDs, and 3 rock CDs.

Q: A sociologist randomly selects single adults for different groups of three, and the random variable…

A: x P(x) 0 0.088 1 0.346 2 0.401 3 0.165 Total 1

Q: Conditional probability distribution Y given that X = 0.5 f(x, y) y -2 -1.0 1/3 -0.5 -1 1/6 0.5 1…

A: Given joint pmf of X and Y is  x y f(x,y) -1.0 -2 1/3 -0.5 -1 1/6 0.5 1 1/6 1.0 2 1/3

Q: Five males with an X-linked genetic disorder have one child each. The random variable x is the…

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Q: The random variable x has a discrete probability distribution with a probability function:  x -2 0…

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Q: A random variable x has the following discrete probability distribution:    x f(x) 0 0.13 1…

A: Given discrete probability distribution table: x f(x) 0 0.13 1 0.17 2 0.22…

Q: An investor has six stocks that she follows each day. The random variable being studied is X, the…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: 2. P(X) = for X = 0, 1, 2 X +2

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Q: Find the wrong answer. The moment generating function Select one: a. is a real-valued function b. is…

A: We can find an answer by using definition of moment generating function

Q: Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd…

A: The random variable x is defined as the number of women ted approaches before encountering one who…

Q: Determine the expected value given the function: f(x) = a≤x≤b). Given that a and b are random…

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Q: and the random variable x is the number in the group Who say that the 0.093 most fun way to flirt is…

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Q: Let X be a random variable with probability distribution as follows: 3 f (x) | 1 1 1 3 Find the…

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Q: Recall the given data. Quality (x) 1 2 3 Total Meal Price (y) 1 45 42 36 9 2 3 Total 3 57 66 159 12…

A: Each probability f(x, y) will be calculated using the formula below. f(x,y)=number of times × and y…

Q: company wants to evaluate its attrition rate, in other words, how long new hires stay with the…

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Q: Conditional probability distribution Y given that X = 0.5 f(x, y) 1/3 y -1.0 -2 -0.5 -1 1/6 0.5 1…

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Q: Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random…

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Q: The table shows the probability distribution of the number of days (x) to complete a construction…

A: Define the probability distribution p(x) for random variable x. The probability distribution p(x) is…

Q: he table shows the probability distribution of the number of days (x) to complete a construction…

A: Given that  Probability distribution  X 1 2 3 4 5 6 P(x)  0.104 - 0.312 0.240 0.098 0.017…

Q: A commuter must pass through five traffic lights on her way to work and will have to stop at each…

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Q: Find the probability of the indicated event if P(E)= 0.25 and P(F) = 0.35. Find P(E or F) if P(E and…

A: Addition rule will applied here

Q: A shipment of 5 television sets contains 2 defective sets. A hotel makes a random purchase of 2 of…

A: Answer:- Given ,  Sample size (n) = 2 Population size (N) = 5 Success size (k) = 2 Using formula,…

Q: A sociologist randomly selects single adults for different groups of three, and the random variable…

A: Conditions for discrete probability distribution: The following requirements should be satisfied for…

Q: The random variable X has the probability distribution given in the following table. 2 3 P(X = 1)…

A: Given problem Given that   Given that  E( X ) = 3.5 ∑X P(X) = 3.5 0.03 + 2a + 0.81 + 4b+ 5c = 3.5…

Q: The population size of Batangas in 2015 is 2,600,000. This increased to 2,908,494 based on the last…

A: Since the question number is not specified, we'll be answering the first question only. Please…

Q: Question Let X be a discrete random variable with the cumulative distribution function: 0 0.3 O C45…

A: Given cumulative distribution function is…

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!