(a) find f(x) (b) Calculate E[X] and V[X]

Q: When a man observed a sobriety checkpoint conducted by a police department, he saw 681 drivers were…

A:

Q: A random variable X can take on only three values: 1, 3 and 0. X takes value 1 with probability and…

A: Given that  Probability mass function of X is x 0 1 3 P(x) 1/12 1/4 2/3

Q: There are 3 traffic lights on the way of the car. Each of them either permits or prohibits moving…

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Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: Given that 40% of fruit flies of fruit flies posses a certain gene. So, probability that a fruit fly…

Q: Variable X assumes 0, 1, 2 and 3 with probabilities 0.3, a, 0.1, and b, respectively. Find a and b…

A:

Q: For a random variable X, suppose that E[X] = 2 and Var(X) = 4. Then (a) E[(4 + x)²] = (b) Var (5+5X)…

A: Given,E(X)=2Var(X)=4we know that…

Q: Suppose that 40% of fruit flies possess a certain gene.  We will randomly select fruit flies until…

A: 40% of the fruit flies posses certain gene. So, probability that a fruit fly posses that gene = 0.4…

Q: When mean number μ of Atlantic hurricanes per year is given: μ=6 Find the probability that in a…

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Q: Find the mean, E[X], and variance, E[X2] - E[X], of a Uniform[a, b] random variable.

A: Given that X follows Uniform (a,b)  We have to find E(X) , Variance and E(X2)-E(X)

Q: A four-sided die has two faces numbered 0 and two faces numbered 2. Another four-sided die has its…

A: Given that, a four-sided die has two faces numbered 0 and two faces numbered 2. i.e.0,0,2,2. Another…

Q: Let probability that a child will be born with black eyes is 1/3, determine the probability that…

A: It is given the probability that a child will be born with black eyes is 1/3 i.e. p=1/3. It has been…

Q: Let X be a non-negative random variable that is not a constant. The product E(1/X) times E(X) is…

A: The question is asking whether the product of the expected value of a non-negative random variable X…

Q: A random sample of size n =5 is taken from a lognormal distribution with parameters u = 0.7 and o…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: When a man observed a sobriety checkpoint conducted by a police department, he saw 691 drivers were…

A: From the information, P(W) denotes the probability of screening a driver and getting someone who is…

Q: Let X and Y be independent, taking on {1,2,3,4,5} with equal probabilities.  E((X+Y)2)=?

A: We have given that X and Y be independent random variables.   The distribution of X is: P( X=x ) =…

Q: When a man observed a sobriety checkpoint conducted by a police department, he saw 660 drivers were…

A: Probability theorem :  P(W)+P(W¯ ) = 1

Q: A survey asked 500 random people how often they use the bathroom on a daily basis. Nineteen percent…

A: Let X=the no.of times a person goes to the bathroom on a daily basis.

Q: Con side that the ten Percent of indlividuals getting tested for the Virus, have the Virus. Now…

A: Let A be the event denoteds the person having virus and B be the event denote the event the person…

Q: Let X and Y be two random variables. Suppose we know E(X) = 7 and E(Y)=3. Let Z = X − Y be a random…

A: Given EX=7 and EY=3.Let Z=X-Y.Then,E(Z)=4

Q: Let X and Y be independent discrete random variables and suppose that X+Y=2. Show that X and Y are…

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Q: The three random variables, a, b and c are independent and each uniformly distributed in the…

A: We can find the roots of any quadratic equation ax2+bx+c=0 using the discriminant as follows:…

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!