Answer Key 1_Mean, Variance and SD of Random Variables (1) (1) PDF

Ateneo de Davao University Senior High School Km. 7, MacArthur Highway Bangkal, Talomo, Davao City A.Y: 2021-2022 Subject: Statistics and Probability Year level: Grade 11 Semester/Grading Period: 2nd...

Ateneo de Davao University Senior High School Km. 7, MacArthur Highway Bangkal, Talomo, Davao City A.Y: 2021-2022 Subject: Statistics and Probability Year level: Grade 11 Semester/Grading Period: 2nd Sem Week/Session: Week 1-2 Topic: Computing the Mean, Variance & Standard Deviation of Random Variables Problem Set 1 w/ Answer key Instruction: Read each item below carefully. You must write your solution in the space provided. In your solution you must show the given, the equation, the process of driving the answer and the conclusion of the problem. Test I. Write D if the random variable is discrete and C if it is continuous. (5 points) 1. the amount of salt in a salt solution C 2. the number of consecutive tails obtained when repeatedly tossing a coin D 3. the number of spikes scored in the championship match during AdDU SHS Intramurals 2016 D 4. speed of a car C 5. number of students in AdDU SHS D Test II. Write P if the data shows a probability distribution. Otherwise, write X. (3 points) 1. X 0 1 2 3 4 P(X) 1/10 2/10 4/10 2/10 1/10 P 2. P(A) = 1/5 , P(B) = 2/5 , P(C) = 1/5 , P(D) = 2/5 X 3. P(5) = 0.11, P(10) = 0.37, P(11) = 0.52 P AdDU Senior High School | Statistics and Probability| Page 1 of 4 Test 3. Number of television X P(X) 1 0.30 2 0.51 3 0.14 4 0.05 1. A study conducted by a TV station showed the number of televisions per household and the corresponding probabilities for each. Find the mean, the variance, and the standard deviation. (X) P(X) X P(X) X-µ (X-µ)2 (X-µ)2 P(X) 1 0.30 0.30 -0.94 0.8836 0.26508 2 0.51 1.02 0.06 0.0036 0.00184 3 0.14 0.42 1.06 1.1236 0.15730 4 0.05 0.20 2.06 4.2436 0.21218 Mean=1.94 Variance=0.64 Standard Deviation= 0.80 2. Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Y be the random variable representing the number of blue balls. Construct the probability distribution of the random variable Y and its histogram. Solve the mean, variance and standard deviation. STEP 1: Determine the sample space. Let R represent the red ball and B represent the blue ball. Sample space: S = {RR, RB, BR, BB} STEP 2: Count the number of blue balls in each outcome in the sample space and assign this number to this outcome. AdDU Senior High School | Statistics and Probability| Page 2 of 4  Possible Outcomes Value of the Random Variable Y (no. of blue balls) RR 0 BR 1 RB 1 BB 2 STEP 3: Identify the probability of each value of the variable X and create a Histogram to represent the data Number of blue balls (Y) Probability of P(Y) 0 1/4 1 1/2 2 1/4 Table 1. The Probability Distribution of the Probability Mass Function of Discrete Random Variable Y HISTOGRAM: AdDU Senior High School | Statistics and Probability| Page 3 of 4 STEP 4: Solve for the mean and variance of the discrete probability distribution. AdDU Senior High School | Statistics and Probability| Page 4 of 4