STA 2023 Test on sections 6.1, 6.2, 7.1-7.3, and 7.5

STA 2023 Test on sections 6.1, , and 6.2.

Classify the following random variable as to whether it is discrete or continuous.

1) The number of runs scored in a baseball game.
A) continuousB) discreteAns = B

2) The cost of a road map.
A) continuousB) discrete Ans = B

Provide an appropriate response.

3) A random variable is
A) generated by a random number table.
B) the variable for which an algebraic equation is solved.
C) a numerical measure of a probability experiment..Ans = C
D) a qualitative attribute of a population.

4) Given the table of probabilities for the random variable x, does this form a probability distribution? Answer yes or no.

x 5101525
P(x)0.1–0.10.30.8 Ans = No

5) True or False: The expected value of a discrete random variable may be negative Ans = True

6) The table of probabilities of the random variable x is given as:

x 0125
P(x)0.50.20.20.1

Find the mean, µ and standard deviation, σ of x. Round answers to one decimal place. Ans = µ = 1.1, σ = 1.5

7) If p is the probability of success of a binomial experiment then the probability of failure is
A) 1B) –pC) 1–pD) p + 0.5 Ans = C

8) A binomial experiment has 6 trials with the probability of success on any trial = p = 0.5. Find the probability of exactly 2 successes in the 6 trials. (Use the binomial probability distribution function.) Ans = 0.2344

9) Assume that male and female births are equally likely and the birth of any child does not affect the probability of the gender of any other children. Find the probability of at most three girls in nine births.Ans = 0.1714 exact Ans = 0.1719 normal approx

10) A test consists of 16 True False questions. If a student guesses on each question what is the mean number of correct answers?...

...infected. What is the probability that 3 randomly chosen client computers serviced by different servers (one per server) will all be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A....

...P(S) The symbol for the probability of success
P(F) The symbol for the probability of failure
p The numerical probability of a success
q The numerical probability of a failure
P(S) = p and P(F) = 1 - p = q
n The number of trials
X The number of successes
The probability of a success in a binomial experiment can be computed with...

...I. ProbabilityTheory
* A branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.
* The word probability has several meanings in ordinary conversation. Two of these are particularly important for the development and applications of the mathematical...

...be able to ONEDefine probability. TWO Describe the classical, empirical, and subjective approaches to probability. THREEUnderstand the terms experiment, event, outcome, permutation, and combination. FOURDefine the terms conditional probability and joint probability. FIVE Calculate probabilities applying the rules of addition and multiplication. SIXUse a tree diagram to organize and compute probabilities....

...variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X)...

...Probability
1.) AE-2 List the enduring understandings for a content-area unit to be implemented over a three- to five- week time period. Explain how the enduring understandings serve to contextualize (add context or way of thinking to) the content-area standards.
Unit: Data and Probability
Time: 3 weeks max
Enduring Understanding:
“Student Will Be Able To:
- Know what probability is (chance, fairness, a way to observe our random world,...

...guys, this is the probability Assignment. Last date for submission is 10 aug...
Q1. What is the probability of picking a card that was either red or black?
Q2. A problem in statistics is given to 5 students A, B, C, D, E. Their chances of solving it are ½,1/3,1/4,1/5,1/6. What is the probability that the problem will be solved?
Q3. A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit the target in 2...

...cloud or the
probability that it will rain, we move from pure simulation to Monte Carlo.
The reason for this distinction is that there may be other ways to deﬁne A
that make it easier to estimate. This process is called variance reduction, since
most of the error in A is statistical. Reducing the variance of A reduces the
statistical error.
We often have a choice between Monte Carlo and deterministic methods.
For example, if X is a one dimensional random variable with...

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