Suppose X is a random variable with the following distribution: xi 1 2 5 10 pi 0.4 0.3 0.2 0.1 Find the expected value of

Q: Let X be the random variable with the following distribution table. 0. 2 3. Sum Pr(X = x) 1/5 I Pr(X…

A:

Q: Calculate ​P(2.5≤x≤4​). b. Determine ​P(x<3​). c. Compute the​ mean, μ​, and the standard​…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If X represents a random variable coming from a normal distribution with mean 3 and if P(X > 4.6) =…

A: From the provided information, Mean (µ) = 3 P (X &gt; 4.6) = 0.3

Q: If Z is a random variable from a standard normal distribution and if P(Z<a)=0.42, then P(Z<-a)=0.58.…

A: If Z is a random variable from a standard normal distribution and if P(Z&lt;a)=0.42, then…

Q: If Z is a random variable from a standard normal distribution and if P(Z <b) D 0.75, then P(Z<-b)…

A:

Q: if the probability distribution for the random variable X is given in the table, What is the…

A: Given that: Xi -2 -1 0 1 2 Pi .1 .2 .4 .2 .1   We will use the formula of expectation:

Q: If Z is a random variable from a standard normal distribution and if P(Z < a) = 0.72, then %3D P(Z <…

A: Therefore,

Q: Let the random variable X represent the number of cars that are used for official business purposes…

A:

Q: If Z is a random variable from a standard normal distribution and if P(Z < a) = 0.7, then P(Z <= a)…

A:

Q: Given that Z is a standard normal random variable, P(-1≤Z≤1.5) is?

A: Using the excel following standard normal probabilities can be obtained as:

Q: 3. Let X be a random variable with the following probability distribution: 5 10 15 20 25 X P(X) 0.5…

A: X 5 10 15 20 25 P(X) 0.5 0.30 0.25 0.25 0.15

Q: Suppose that T is a random variable with the following probability distribution: 3. Т -7 -3 1 3 f(t)…

A: From the given information,

Q: Given that Z is a standard normal random variable, P(-1.0≤Z≤1.5) is?

A:

Q: Find the following probabilities for the standard normal random variable z: (a) P(-1.08 –0.4) =

A:

Q: Let X be a random variable with expected value 2, and let Y be a random variable with expected value…

A: Recall:      Let X and Y be the random variable with expected values  then…

Q: 10. The random variable X, representing the number of chocolate chips in a cookie, has the following…

A:

Q: Consider a random variable with the following probability distribution:  X          P(X) 0…

A: The table shows the probability distribution of X.

Q: If X represents a random variable coming from a normal distribution with mean 4 and if P(X > 5.1) =…

A:

Q: Suppose the random variable Z follows a standard normal distribution. Then the value of P(-2.21 <…

A: The Random variable Z follows a standard normal distribution We need to calculate

Q: If X represents a random variable coming from a normal distribution and P(X 6.5) = 0.59. True O…

A: It is given that P(X&lt;6.5)=0.41.

Q: A random variable X has the probability distribution given in the following table: 2 3 4 5 6 P(X =…

A: When random variable X has the probability distribution then sum of the probabilities must be equal…

Q: 2) For a standard normal random variable, find the point in the distribution in which 11.9% of the…

A: The given probability value is 0.119=11.9100.

Q: Find the expected value E(X) of a random variable X having the following probability distribution.…

A: The expected value of any discrete random variable X with probability distribution PX=x, is given…

Q: For the random variable Z follows a standard distribution, find P(-1.2<Z <2.1)

A: Given data: For the random variable Z follows a standard distribution, To find ; P(-1.2&lt;Z&lt;2.1)

Q: If X represents a random variable coming from a normal distribution with mean 5 and if P(X> 6) = 0.4…

A: The mean is 5.

Q: Consider the probability distribution of a binomial random variable X given below: 1 2 3 4…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Let x be a random variable with the following probability distribution 2 4 P(x) 0.3 0.2 0.3 k 0.1…

A: answer the correct option is A a. 2.7 and 2.1

Q: Suppose the random variable X has the following probability distribution -1 1 P(X=x) 0.2 0.3 0.3 0.2…

A: Given data,   1)P(X&lt;2)=?

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

A:

Q: if the probability distrobution for the random variable X is given in the table  what is the…

A:

Q: riable X has the following probability distribution; x 0 1 2 3 P(X) 0.1 0.4 0.3 0.2 then the mean…

A: The formula of the mean is:

Q: Suppose that the random variable z, shown below, represents the number times . P(x) represents the…

A: a) The random variable x represents the number of times a randomly selected person having received…

Q: Find the expected value for the random variable: X 1 2 4 P(X) 0.21 0.25 0.11 0.43 E(X) =

A:

Q: Find E(X), Var(X), and the standard deviation of X, where X is the random variable whose probability…

A:

Q: Let X be a random variable with range {20,30,50} and probability distribution P(X=20) = 0.25,P(X=30)…

A:

Q: The random variable X is described by the following probabilities. i 1 4 P(X = i) = Pi 0.5 0.4 0.05…

A: The Expected Value is given as: Expected Value = ∑Xpi=0×0.5+1×0.4+3×0.05+4×0.05=0.75

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

A: Given,

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

Q: If X represents a random variable coming from a normal distribution with mean 5 and if P(X>6.1)=0.2,…

A: Given: Meanμ=5, P(X&gt;6.1)=0.2

Q: Let X be the random variable with the following distribution: x: 1 2 3 4 5  P(X=x): k 0.04 0.3 0.2…

A:

Q: In which probability distribution would a random variable XX have E(X)=λE(X)=λ?

A:

Q: The following is a probability distribution for a discrete random variable X. 0 1 2 5 P(X) 0.1 0.2…

A: The formula of the expected value is,

Q: Suppose the random variable Z follows a standard normal distribution. Then the value of P(-2.21 < Z…

A: According to the given information, we have P(-2.21&lt;Z&lt;-1.39)

Q: If the probability distribution for the random variable X is given in the​ table, what is the…

A: Given the probability distribution for the random variable X is: xi −1 2 4 pi…

Q: Let X be the random variable with the following distribution: x: -2 3 5 P(X=x): 0.3 0.2 0.5 Find…

A:

Q: The following is a probability distribution for a discrete random variable X. X -1 0 1 10 P(X) 0.2…

A: It is an important part of statistics . It is widely used . Expected value of X is obtained by…

Q: A discrete random variable can assume 5 possible values, as listed in the accompanying probability…

A: From the provided information, x -5 0 25 P (x) 0.20 0.30 0.10

Q: Suppose the random variable Z follows a standard normal distribution. Then the value of P (Z< -3.39)…

A: Let Z be the standard normal variable with mean μ=0 and standard deviation σ=1 Z~N(0,1)

Q: If x is a binomial random variable with n = 10 and p = 0.8, the standard deviation of x is…

A:

Q: Suppose that the random variable z, shown below, represents the number times. P(z) represents the…

A: Given data,

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!