Calculate the mean (mu)  and variance (sigma squared) of the probability distribution

Q: Illustrate probability density function of a normally distributed random variable?

A: f(x)=12πσ2e-(x-μ)22σ2   -∞<x<∞     X~N(μ,σ2)

Q: Compute the Mean, Variance and Standard Deviation of the Probability Distributio

A: Here, Height, x Frequency, f fx (x-x) (x-x)2 f.(x-x)2 57 1 57 -4.82 23.2324 23.2324 59 3 177…

Q: The mean of a standard normal probability distribution

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Q: Find the mean and standard deviation  of this random variable.

A: Define the Random Variable, X : Number of tickets bought by a individual Given that, X ~ Discrete…

Q: Calculate the standard deviation value by finding the value a in the table so that the random…

A: From the given information, x 0 1 3 4 f(x) 2/5 a 3/20 7/20 The value of a is obtained…

Q: What requirements are necessary for a normal probability distribution to be a standard normal…

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Q: If four coins are tossed simultaneously, what is the probability distribution of the random variable…

A: From the provided information, Total outcomes tossing four coins simultaneously = 42 = 16

Q: What is a chi-square distribution?

A: Chis square distribution is used on standard normal random variable using k degrees of freedom , it…

Q: what is a gaussian distribution?

A: Gaussian distribution (also known as normal distribution) is a bell-shaped curve, and it is assumed…

Q: What does standard deviation measure in a probability distribution

A: In simple words, Standard deviation measures the variability of all possible outcomes of a…

Q: Consider a carnival game where a player is given two chances to throw a ball to hit a moving target.…

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Q: The traffic probability distribution carry . .categories for Variance to Mean Ratio (a = 1) *

A: According to question, fill in the blanks "The traffic probability distribution carry .....…

Q: Determine the Binomial distribution for which the mean is 4 and variance 3 and find its mode.

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Q: The mean value of the Poisson probability distribution is numerically equal to its standard…

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Q: Which distribution can be fully described by its expected value and standard deviation? O…

A: The normal distribution is fully described by its expected value and standard deviation.

Q: An oil company conducts a geological study that indicates that an exploratory oil well should have a…

A: Geometric distribution: The probability mass function of Geometric distribution is P(n) = p(1 - p)n…

Q: 20. What does standard deviation measure in a probability distribution?

A: Probability distribution: A statistical function which describes the all possible values of the data…

Q: Give 1 real life situation where the concept of random variables is applicable and construct its…

A: A random variable is a variable whose values depend on outcomes of a random experiment. It is…

Q: Define Probability Distribution of a Discrete Random Variable?

A: The probability distribution of a discrete random variable is a table that mentions all the possible…

Q: A normal probability table uses the standard normal curve to determine areas of probability by the…

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Q: Write and sketch the pdf of the Gaussian (normal) distribution for different mean and variance…

A: Probability density function of normal distribution: A continuous random variable X is said to…

Q: Compute the mean and variance of a random variable whose distribution is uniform on the interval [a,…

A: Given: Consider a random variable X following Uniform distribution with the range a and b. The…

Q: Find the mean of the random variable X.

A: Let X is a continuous random variable. The probability density function is given as,…

Q: The number of telephone calls coming into Grace Floral Shop to place orders averages 3 per minute.…

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Q: Provide an interpretation of the mean (or expected value) of a discrete random variable.  Give an…

A: The Mean of a discrete random variable X is weighted average of all the possible values that a…

Q: Distinguish between the Binomial and Poisson probability distributions.

A: Answer:- Binomial distribution describes the distribution of binary data from a finite sample. Thus…

Q: A survey shows the probability of the number of automobiles that families in a certain housing plan…

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Q: . What is the expected value and what does it measure? How is it computed for a discrete probability…

A: In the theory of probability, the expected value of a random variable X denoted EX is a…

Q: Table below presents the joint probability distribution associated with data obtained in a study of…

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Q: Define PPS (probability proportionate to size)

A: PPS (probability proportionate to size)    It is a method of sampling.

Q: Use the probability distribution table to find: a) Expected value (mean average) b) Standard…

A: Given, Probability distribution: X 1 2 3 4 5 P(X) 0.13 0.15 0.35 0.31 0.06   the required…

Q: Define the chi-squared distribution?

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Q: The mean value of the Gaussian probability distribution is numerically equal to its variance. True…

A: The Gaussian probability distribution has two parameters mean and variance.

Q: Calculate the expected value, the variance, and standard deviation where X is the number of tails…

A: X=the number of tails n=sample size=3p=probability of success=12=0.5So, X follows a binomial…

Q: Derive the mean and the variance of Poisson Distribution

A: The p.m.f. of Poisson distribution is given by P(X=x)=e-m  mxx!        ; x=0,1,2,....…

Q: Determine the required value of the missing probability to make the distribution a discrete…

A: To find the value of P(4) we will use the fact that sum of probabilities of possible outcome is…

Q: how can you use the concepts of the mean variance and standard deviation of the probability…

A: Mean: Mean for a probability distribution is the average expected return from the gamble It means…

Q: Determine the cumulative distribution of the random variable J

A: The given probability function f(j) can be described as J -1 0 1 f(j) (-12/2)-(-1/8) = 0.625 0…

Q: b) Explain why the statistical properties of a random variable (RV) is expected to change if RV is…

A: The answer is explained below as follows.

Q: Calculate the probability of a sample mean being at least as high as a specified value when σ is…

A: The formula for standard score of sample mean is given below: A sample of size n is selected from…

Q: What is the capital letter gamma denoting a gamma function? What does it do in a continuous…

A: Gamma (uppercase Γ, lowercase γ) is the third letter of the Greek alphabet. In the Greek numerals…

Q: A description of the distribution of the values of a random variable and their associated…

A: Given that, A description of the distribution of the values of a random variable and their…

Q: The central limit theorem states that the distribution of the mean of independent, identically…

A: Given that, random variable is independent and identically distributed.

Q: 2. The probability that a customer will buy 1, 2, 3, 4, or 5 items in a grocery store are 3 1 1 2 3…

A: First, it is required to find the mean of the probability distribution. The mean is computed by…