True or False 1. The sum of the probabilities of all values of the random variable must be equal to 1 2. The capacity of water dams in a region is an example of discrete random variable 3. TRUE

Q: X is a chi square random variable with 11 degrees of freedom. What is the value of x if P(X > x) =…

A: Given information- We have given that, X is a chi-square random variable. Degree of freedom, df = 11…

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: The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway…

A: The probability that the speed of a car is at most 29 mph is 0.727, which is obtained below:…

Q: Consider that the population of 45,000 students includes 6,000 foreign students and 39,000 domestic…

A: Given : Population size (n) =4500 Population includes 6000 foreign students and 39000 domestics…

Q: 2) For passengers flying on a given airline, the expectation of the weights of suitcases is 10 kg…

A: Solution: Given information: n= 100 sample size  μ=10 kg Population mean σ2=5 kg2 Population…

Q: When testing for COVID infections, it can be more efficient and less expensive to combine samples.…

A: Given probability that a combined sample tests positive given that the individual sample infection…

Q: How can we use discrete random variables in statistics?

A: Solution: Discrete random variable: A variable is said to be discrete if it takes the positive…

Q: Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You…

A:

Q: Dominoz Airlines: Dominoz Pizza decides to expand into the airline industry. Knowing that peopie are…

A: 8. Note: " Since you have asked multiple sub-parts, we will solve the first three sub-parts for you.…

Q: A random variable X can takes values 1,2,3 or 4 with probabilities 0.6,0.2,0.15 and 0.05…

A:

Q: Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You…

A: Follow Geometric distribution - Let X be number of trials to get first success or X ~ Geo(p)

Q: Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You…

A: It is an important part of statistics. It is widely used.

Q: Suppose, you are running an experiment that has two outcomes, namely 'success' and 'failure'. You…

A: Given: The value of variance of number of experiments required for first success is, σ2=20. The…

Q: Suppose you throw two dice and take the sum as a discrete random variable. Let us assume you take a…

A: When you throw two dices together, each dice will show a number ranging from 1 to 6 on the side…

Q: A random sample of size 100 is taken from an infinite population having the mean 76 and variance 256…

A:

Q: If the random variable x is distributed through the Binomial(n,0.5), if the mean of x =3,then the…

A: We have to find variance of x...

Q: This problem involves the flipping of a fair coin. Assume that the coin is flipped 4 times, and the…

A: It is given that the coin is tossed 4 times.Thus, when a coin is tossed 4 times a person can get 0…

Q: If the random variable X is defined as the number of successful free throws from 3 throws, the…

A: From the given information we find probability

Q: If the conditional mean of one random variable given another is zero, then the two random variables…

A: Given that  If the conditional mean of one random variable given another is zero, then the two…

Q: The time (in hours) required to repair a machine is an exponentially distributed random variable…

A: Given that λ=1

Q: If the random variable X is distributed according to the Binomial distribution Bin(5,0.6) then…

A: Let X represent random variable   X~ Binomial(5, 0.6)

Q: "If for low values of random variable we have high frequencies and for high values of random…

A: If for low values of random variable we have high frequencies and for high values of random variable…

Q: Two dice are rolled once at the same time. If it is known that X is the result of the sum of the…

A: The objective is to find the expected value and variance of X when two dice are rolled X is rv…

Q: If X is a binomial random variable with n = 15 and p = 0.3, we can use the normal approximation? О…

A:

Q: X is the Binomial Random Variable which counts the number of students who passed an exam. If the…

A: Here, n=46 and p=0.89.

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

A: From the given information,

Q: If you fail to reject the null hypothesis at the 5% level, then the probability that you are wrong…

A: The type I error is defined as the rejecting the null hypothesis when actually it is true.

Q: Suppose a binomial random variable consists of 10 trials with a success of probability 0.35. What…

A: Given that n = 10, p =0.35

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

A:

Q: Suppose that 100 items are sampled from a manufacturing process and 3 are found to be defective. Let…

A: The binomial distribution is a discrete probability distribution where we have a series of n…

Q: If x is a random variable that has a uniform distribution in the interval [1,7].[1,7]. What is the…

A: Solution-: Let, X- be the the random variable Given: a=1, b=7 We find, P[the random variable x…

Q: In a game of craps you end up rolling 2 fair dice. Now, whether you win or lose depends on the sum…

A: a) Two dices are rolled and winning or losing the game depends on the sum of the numbers appearing…

Q: Can the idea of joint random variables apply to more than two variables or is it just strictly like…

A: Joint random variables  In Joint random variables we generally takes two random variables X and Y we…

Q: 3. The ratio to the probabilities of 3 successes and 2 successes among 5 independent trials 3 Find…

A: Let us consider the no. of success to be denoted by X, which follows binomial distribution i.e. X…

Q: Explain what it means for two random variables to be independent, both mathematically and in…

A: In real world, we are surrounded with a lots of problems involving uncertainty. Random variables…

Q: For the probability distribution of a discrete random variables, the probabilities of any single…

A: The probability can't be exceed than 1 for any distribution.

Q: If our value is not biased, the probability that the sampling error will be a negative value (or the…

A: Here use basic of sampling error and sampling distribution

Q: Determine if the random variables X and Y are statistically independent or not. NO NEED SOLUTIONS

A:

Q: A random sample of size 225 is taken from a population with a mean of 10 and variance 4. Find the…

A: Given n=225 Mean=10 Variance=4

Q: 2. Suppose X is a normally distributed random variable with a mean of 9.00. If the probability that…

A:

Q: We are playing a game. I randomly say a whole number and if you guess its parity (odd or even)…

A: Considering even and odd are equally likely, the probability of correct guess = 0.5       The game…

Q: Consider you toss two dices separately, and you get whatever the number above the dice. (ou know…

A: The two dice are thrown having different values of outcomes.

Q: If you sum the probabilities of the possible values of a discrete random variable, the result always…

A: The requirements for a discrete probability distribution are,

Q: A random variable that is normally distributed with μ = 210 and σ = 20. What is the probability that…

A: Mean = 210 Standard deviation = 20 Sample size = 4

Q: A customer service representative must spend different amounts of time with each customer to resolve…

A:

Q: Fundamentally, we saw probability in the Statistics Lifecycle as the underlying tool required in…

A: We need to answer  Why is it that we need probability? Why can’t we go straight from using the…

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…

Q: The mean of a random variable will be negative if all possible values of the random variable…

A: According to the given information, we haveThe possible values of the random variable are negative.

Q: Suppose X is a binomial random variable where the probability of success on each trial is 0.08 and…

A: Obtain the probability that X is greater than or equal to 8. The probability that X is greater than…

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.