Statıstıcs I Final 2. Deneme Sınavı

In the classical probability approach to assign a probability to an event, the assumption is that all the outcomes have the same chance of happening. Pick up a six-sided fair die, there are six numbers on each face of the die as 1, 2, 3, 4, 5, and 6. Classical probability says that each side of the die has the same chance  to come face up if this die is thrown. Since there are 6 possible outcomes of throwing a six-sided fair die probability of obtaining any number represented on the faces of this six-sided fair die is 1/6. We can formularize this by following equation:

Probabilityof an Event = Thenumber of timestheevent can happen
/Total number of possibleoutcomes

A random experiment is any process that leads to two or more possible outcomes, without knowing exactly which outcome will occurIn a random experiment, Although we do not know which outcome will occur, we are able to list or describe all of the possible outcomes. The set of all possible outcomes is important to understand the random experiment. Therefore, it is called a sample space, which is restated below as a definition.

For X which is a continuous random variable that is uniformly distributed and takes values between 3 and 9, the minimum value of the random variable X is 3 (it’s the value of a) and the maximum value is 9 (it’s the value of b). Then X~U (a=3, b=9) and the probability density function of the continuous random variable X is defined as, f (x) = 1/(b - a) = 1/(9 - 3)= 1/6 for 3?x?9. The mean is equal to (9 + 3)/2 = 6. The answer is E.

Categorical variables and data can be either nominal or ordinal.
The question about climate change, with possible responses “natural”, “manmade” or “don’t know/can’t answer” is a nominal categorical variable, as is the variable “country” - there is no ordering in the categories
of these variables. By contrast, exam grade is an ordinal categorical variable, since its categories are ordered: A is better than a B, B is better than a C, and so on.

m = E(X) = Int(-sonsuz , sonsuz)(....) = Int(20, 60)(x * f(x) dx) = Int(20, 60)(x * 0.025 * dx) = girdi(20, 60)((1/2) * x2 * 0.025) = (1/2) * 0.025 * (3600 - 400) = 0.25 * 160 = 40 ; V(X) = E(X - m)² = Int(-sonsuz , sonsuz)(....) = Int(20, 60)((x - m)² * f(x) dx) = Int(20, 60)((x - 40)² * 0.025 * dx) = girdi(20, 60)((1/3) * (x - 40)³ * 0.025) = (1/3) * 0.025 * (8000 - (-8000)) = (1/3) * 0.25 * 1600 = 400/3 ; sd = (400/3)^1/2 = 20 / 3^1/2 ; . pg. 184. Correct answer is E.

1. Right skewed

2. Mode

3. Median

4. Mean

The correct answer is C.

Note that there are five different letters, namely U, S, A, L, Y and that the letters U and L are used twice. If all the seven letters in the given word were different, the total number of arrangements would be 7!. Since all the arrangements of the two letters U1 and U2 , and all the arrangements of the two letters L1 and L2 should be counted only once, it follows that the answer is 7!/ 2!2! =15. The correct answer is C.

The mean of the continuous random variable X;

We have to compute zero red balls and 1 red ball.

P(x=0)=C(4,0)*0.6⁰*0.4⁴=0.4⁴

P(x=1)=C(4,1)*0.6¹*0.4³=2.4*0.4³

P(x=0)+P(x=1)=2.4*0.4³+0.4⁴=0.4³(2.4+0.4)=2.8*0.4³=0.1792=0.18

Range is the difference between the lowest and the highest score in a data set that's why the correct answer is B.

Simple bar chart is used to represent discrete values for each category for a given variable on x-axis (horizontal). The y-axis (vertical) shows the actual numbers that are the bar heights for the corresponding category.

A major difference between continuous and discrete random variables is the former takes on uncountable and infinite number of possible outcomes in a given interval. Hence the range of continuous random variable X comprises all real numbers in an interval. In addition to the above given illustrations, water consumption amount in a household, weights of people in a population, the speed of wind in a open certain area, waiting time in a supermarket, checkout lanes or load on a bridge are the few examples for continuous random variable for real world applications. From these examples it’s clear that random variable X can take unaccountably infinite values. To describe such physical structures through continuous random variables density functions are utilized. Therefore, in contrast to discrete random variables, probabilities in continuous random variables can be determined from the area under probability density function (pdf) which is represented by f (x).

Ratio scales of measurement, in addition to having all properties of the ­interval scale, have a natural or zero-valued base value that cannot be changed. For example, an individual’s age, weight, height.

In economics, the tendency of a foreign currency versus Turkish Lira may also be analyzed by a simple line chart, which may show a long term increase in the value of Turkish Lira against the foreign currency of interest. Therefore, an investor may decide that the power of Turkish Lira is increasing and it is high time to make an investment in Turkey.

I. The complement of an event A is the set of all basic outcomes in S that do not belong to A. (True)

II. The union of events A and B is the set of all elementary outcomes that belong to both sets. (False, The intersection of events A and B is the set of all elementary outcomes that belong to both sets.)

III. The intersection of events A and B is the set of all elementary outcomes that belong to at least one of the sets A and B. (False, The union of events A and B is the set of all elementary outcomes that belong to at least one of the sets A and B.)

The answer is A.

This is how we formulate the probability: P(A1? A2 ) = P(A2|A1 )P(A1 ) = P(A1 )P(A2|A1 ) 

This is how we calculate the probability of drawing two yellow cards: 6/36.5/35=1/42= 0.02381

A discrete random variable typically comprises of a counting concept. On the other hand, continuous random variables represent entire infinite values in an interval. For that reason, continuous random variables are commonly measured instead of counted. The speed of a plane, waiting time of customers at a bank’s call center, rainfall amount in a given day and inter arrival time between two customers which arrive to the post office are commonly cited examples for continuous random variables.

arithmetic mean : m = 720 / 5 = 145 ; s = ((45² + 25² + 25² + 35² + 55²) / 4)^1/2 = ((2.025 + 625 + 625 + 1225 + 3.025) / 4)^1/2 = (7.475 / 4)^1/2 . pg. 111 . Correct answer is D.

16 numbers ; k = 16 x 80 / 100 = 12.8 not integer ; (?k? + 1) = 12 + 1 = 13 ; P(13) = 2.9. pg. 117. Correct answer is B.