If the standard deviation of a Poisson random variable X is 2, then find the probability that X is strictly positive.

Q: Suppose X is a random variable with possible values 1,-4 and 4 and with respective probabilities…

A: We have the random variables with probabilities. x 1 -4 4 P(x=x) 0.15 0.48 0.37 WE Know E(x)…

Q: If X is a discrete random variable, and it’s PMF function is given by f(x). What is the correct way…

A: According to the provided information, X is a discrete random variable, and it’s PMF function is…

Q: Find the mean and standard deviation for the binomial random variable x with n = 30 and P = 0.6.

A: Given: n=30p=0.6

Q: If continuous random variable X is normally distributed, with µ = 8.7 and σ = 3.9, what is P(X >…

A: Given information: The value of µ is 8.7. The value of σ is 3.9. To find: The value of PX>14.

Q: otherwise If the expected value of the random variable X is 1/3. Find the values A and B.

A: Here use property of probability distribution function

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: Assuming a coin is unbiased (P(X=1)=P(X=0)=0.5), work out the theoretical mean and standard…

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: 2n- 50 and p= 0.45

A: Given, Let, n =number of trials p =the probability of success q=1-p

Q: The number of people arriving at a particular bank teller is approximately distributed as a Poisson…

A: Solution: Let X represents the number of people arriving at a particular bank teller.  The average…

Q: The covariance of two random variables is always a number between -1 and 1 True False

A: In this case, we need to find the correct option.

Q: |If the expected value of the random variable X is 1/3. Find the values A and B.

A:

Q: The random variable X has a binomial distribution with n = 6 and p = 0.3. Calculate: P (X 2 5)

A: Givenn=6p=0.3x~Binomial(n=6,p=0.3)P(X=x)=(nx)×px×(1-p)n-x ;  x=0,1....,n

Q: The number of requests a particular server receives during 1 second is modeled by a Poisson random…

A: Explanation: The server receives 1000 requests per second on average It means,  1 second = 1000…

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

A:

Q: Assume a random variable X follows a Poisson distribution with a mean μ=2.6 P(X≤3)=  Round each…

A: Given : a random variable X follows a Poisson distribution with a mean μ = 2.6 The formula for…

Q: The number of students who fail per semester is often modeled as a Poisson random variable. Assume…

A: Solution. As per guidelines we answer the first three subparts only.

Q: If E denotes the expectation the variance of a random variable X is denoted as

A: Here use mean and Variance of random variable X

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

A:

Q: Since P {X = -6} = 1/6, P {X = 3} = 1/3, P {X = 4} = 1/2  , Calculate the expected value and…

A: Expected value:E(X)=∑xipi=-616+313+412=2

Q: Assume a random variable XX follows a Poisson distribution with a mean = 1.1. Find P(X=4)P(X=4).…

A:

Q: Let the random variable X fit the binomial distribution with p=1/2 , n=3 parameters. Plot the…

A: Given Data: n=3 p=0.5   Distribution function is also known as cumulative function

Q: If a random variable that follows exponential distribution shows that P(X2000)=0.7, Then P(30002000)…

A: Exponential probability distribution has memoryless property i.e. P(X &lt; a   | X &gt; b) = P(X…

Q: 4. For a linear combination of n random variables, find its expectation and variance.

A:

Q: Let X be a binomial random variable with n=7 and p=0.1, then The variance of X is 0.63 P(X>1)=…

A: Given: n=7 and p=0.1 Then, the variance isVariance=np1-p=70.11-0.1=70.10.9=0.63

Q: For a poisson random variable (x) with a mean of 6.6; P(X≤1)?

A: Solution:From the given information, the random variable x follows Poisson distribution with mean as…

Q: If a random variable X has a Poisson distribution with P(X = 1) 2P(X = 2). What is P(X = 3)? %3D 2

A: Hence,  Option (a)  e^-1/6 , is the correct✅ choice.

Q: For a poisson random variable (x) with a mean of 3.3; p(x&gt;11) =?

A: The value of P (X &gt;11) is obtained below:It is given that in the value of mean is 3.3 that is…

Q: Which of the following random variables is continuous?

A: A variable is said to be continuous if it can take any value in an specified interval.

Q: )A random variable is defined as 1/70 (2x − 1); X = - 1,2,3,4,5,6. Construct the probability…

A: Total no of observations (n) = 6 X = 1, 2, 3, 4, 5, 6 P(X=x) = (2x-1)/70

Q: If Z is a standard normal random variable, then what is the probability that Z&gt; 1.5 or Z&lt;…

A:

Q: For a discrete random variable which takes on nonnegative values (0, 1,2,3, . . .) such as the…

A: whether the given statement is true or false

Q: In a Binomial Distribution consisting of 4 independent trials, probabilities of 2 and 3 successes…

A:

Q: If the random variable X has a Poisson distribution where the lambda equals 7, Then the probability…

A: Givenλ=7x~poisson(λ=7)P(X=x)=e-λ×λxx!   x≥0

Q: The joint distribution of the random variable X and Y is given in the following table:

A: From the total probability condition, ∑x∑yPx,y=1 Consider,…

Q: The number of accidents at a certain intersection is a Poisson random variable. The probability that…

A: we have given that  The probability that there are 2 accidents in any given week is 3 times as much…

Q: Suppose X is a random variable with possible values -2,3 and 1 and with respective probabilities…

A: Given information, X -2 3 1 P(X) 0.22 0.35 0.43 Mean: X -2 3 1   P(X) 0.22 0.35 0.43…

Q: .If a random variable X assumes the values 0 and 1 with

A: From the given information,

Q: A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12 times, what is the…

A: We have given that A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12…

Q: If a Poisson random variable has a μ = 0.9. Use the Poisson table (Table 2) to find the following…

A: From the provided information, µ = 0.9 The probability distribution function of Poisson distribution…

Q: Suppose that random variables X₁ and X₂ have exponential distribution with expected value and ,…

A: i. Given information: X1 and X2 are exponential distribution with expected value of 1/2 and 1/3. X1…

Q: 1. Let Z be a standard normal random variable. Calculate the following probabilities.

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

Q: According to a candy​ company, packages of a certain candy contain 24​% orange candies. Find the…

A: A candy​ company, packages of a certain candy contain 24​% orange candies. That is, p=0.24. The…

Q: Let X1 and X2 be independent standard normal random variables. Show that the joint distribution of

A: Given information: It is given that X1 and X2 are independent standard normal random variables.

Q: Let X be a Poisson random variable with parameter 2. (i) What is the probability P(X > 1)? (ii) What…

A: Solution: From the given information, X follows Poisson distribution with parameter 2. That is, λ=2.…

Q: Which one of these variables is a continuous random variable?

A: Continuous variables are those variables which can take any value in an specified interval. Discrete…

Q: If the number of hurricanes that hit a certain area of the eastern United States per year is a…

A:

Q: For the probability distribution of a discrete random variables, the sum of the probabilities of all…

A: For the probability distribution (discrete) to be valid, the following conditions must follow- Each…

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!