Statıstıcs I

Yanıt Açıklaması: This is a permutation with  repeated items. If all the seven letters in the given word were different, the total number of arrangements would be 6!. Since all the arrangements of the two letters C1 and C2 , and all the arrangements of the two letters M1 and M2 should be counted only once, it follows that the answer is: 6!/2!2!=180

Yanıt Açıklaması: If this is a probabilty distribution than the sum of all probabilities must be equal to 1. Thus 0.2+0.3+0.1+a+b=1 which means a+b=0.4, thus b=0.4-a. Also it is given that the mean of X is equal to 2.8. Mean=Sum((X=x)P(X=x)) 2.8=(1*0.2)+(2*0.3)+(3*0.1)+(4*a)+(5*b) 2.8=1.1+4a+5b 1.7=4a+5b=4a+5(0.4-a) 1.7=2-a 0.3=a

Yanıt Açıklaması: Each dice has a possible outcome of 6 in total {1,2,3,4,5,6}. If they are thrown at the same time the possible outcome would equal to 6*6 = 36. The answer is D.

Yanıt Açıklaması: Int(25, 35)(f(x) dx) = 0.04 * x = 0.04 x (35 – 25) = 0.04 * 10 = 0.4. pg. 180. Correct answer is C.

Yanıt Açıklaması: z = (x – m) / sd ; (210 – 270) / 90 = -2/3 ; P(z <= (-2/3)) = P(z >= 2/3) = 0.5 – P(z = 2/3) . pg. 200. Correct answer is B.

Yanıt Açıklaması: Let us denote the Italian models by X1 and X2, the Turkish models by Y1, Y2, and Y3. Then, there

Yanıt Açıklaması: Grades like "AA" or "BB" taken from a course is an ordinal categorical variable.

Yanıt Açıklaması: Discrete random variables have only a countable number of separate values such as 0, 1, 2 , 3... etc. For example, the number of students in a class for certain day or the number of customers in a supermarket after 5:00 PM are cases for discrete random variables since these variables are finite and countable. Conversely, continuous random variable can take entire infinite values in a given interval. Because of this reason, continuous random variables are commonly measured instead of counted. For instance, waiting time for customers in a supermarket cashier line and travel time of a bus between two points are examples for continuous random variables. The correct answer is D.

Yanıt Açıklaması: The sum of all probabilities must be equal to 1, if it is a probability distribution table. Thus 3k+5k+8k+3k+k=20k=1 then k=1/20=0.05

Yanıt Açıklaması: I. The exponential random variable is frequently used to model the time interval between two events. (True) II. The exponential random variable is defined with a parameter ?. (True) III. The exponential random variable X defines the time interval between two independent events. (False, the exponential random variable X defines the time interval between two consecutive events.) The answer is C.

Yanıt Açıklaması: P(A)=0.40  P(U/A)=0.10  P(U/A).P(A)=0.04 P(B)=0.35  P(U/B)=0.20  P(U/B).P(B)=0.07 P(C)=0.25  P(U/C)=0.05  P(U/C).P(C)=0.0125 P(U)= 0,04+0,07+0,0125=0,12 P(A/U)=0,04/0,12=0,33

Yanıt Açıklaması: You get the mean score if you divide the total scores by the number of scores.So the correct answer is D.

Yanıt Açıklaması: When order is important, we call the arrangements of a finite number of distinct objects a permutation . For example, there are a total of 3!=6 different ordered arrangements of the three letters A,B, and C. If there are four letters (W,X,Y,Z) there are a total of 4!=24 different ordered arrangements.

Yanıt Açıklaması: 0,01

Yanıt Açıklaması: IQR = Q3 - Q1 = P(75) - P(25)=40-20=20

Yanıt Açıklaması: In this problem exponential random variable X represents the physical examination time. Also, the mean μ = 25 minutes of the physical examination time, therefore λ=1= 1 =0.04μ 25 The probability density function is as follows, f (x) = (0.04) e-0.04x, x ≥ 0 Therefore X ~ Exponential (λ = 0.04) and to find the probability that the physical exam duration takes less than 20 minutes P (X < 20). P(X<20)= ∫20=(0.04)e−0.04xdx=−e−0.04x 20 =−(e−0.8 −1)=0.5500

Yanıt Açıklaması: The variance (σ2) of the continuous uniform random variable X between a and b, X ~ U (a = 5, b = 19) can be calculated from these formula,(b−a)2 (19−5)2 σ2 =V(X)= 12 = 12 =16.33Standard deviation, σ = 4.041

Yanıt Açıklaması: The Poisson distribution is widely used for discrete probability distribution which is used to model the number of outcomes occurring during a specified time interval or in a definite region.

Yanıt Açıklaması:

Yanıt Açıklaması: The measures of skewness are another kind of descriptive statistics and give information about the shape of distribution of the observations. A data set which is not symmetrically distributed is called skewed.