Suppose that we have a discrete random variable Xa with PDF and CDF fa(x) and Fa(x), and a continuous random variable X. with PDF and CDF f.(x) and F.(x). Now we create a new random variable X in the following way. We have a coin with P(H) = p. We toss the coin once. If it lands heads, then the value of X is determined according to the probability distribution of X4. If the coin lands tails, the value of X is determined according to the probability distribution of Xe. This is called Mixed Random Variable formulation. Find E[X²].

Q: Suppose a coin is tossed. Let X be the random variable representing the number of heads find the…

A: x P(x) x.P(x) 0 450 0 1 850 850 2 1650 3250 3 1450 4250 4 650 2450 5 250 1050 Total…

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: Suppose X takes the value 1 with probability P, and the value 0 with probability (1-P). The…

A: Variance formula is:

Q: Find E(Y), the expected value of Y. Give your answer as a fraction in its simplest form.

A:

Q: From a sack of fruit containing 3 oranges, 2 apples, and 3 bananas, a random sample of 5 pieces of…

A: 0.070Explanation:Step 1:  correlation coefficient  between X and Y is given by…

Q: Suppose two independent discrete random variables X₁ and X2. Both follow a discrete distribution…

A: It is given that: PX1=1=PX2=1=p1=0.5PX1=2=PX2=2=p2=0.3PX1=3=PX2=3=p3=0.2 The variables X1 and X2 are…

Q: If X and Y are any random variables with COV(X, Y) = 0.25, o = 0.36, and o = 0.49, then the…

A: From the given information, Covx,y=0.25         σ2x=0.36         σ2y=0.49 Thus,

Q: f X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find…

A: Given:    X1, X2 are two independent exponential random variables with respective parameters λ1 and…

Q: The correlation coefficient of two random variables X and Y is -0.251 and V(X) = 3 and V(Y) = 5.…

A:

Q: An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of “heads” (h) and “tails” (t)…

A: In this case, the random variable R defines the number of heads.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.