1 FALL 2015 STA 2023 INTRODUCTORY STATISTICS-1 PROJECT INSTRUCTOR: VENKATESWARA RAO MUDUNURU EMAIL: VMUDUNUR@MAIL.USF.EDU nV IMPORTANT: You should submit the answers for this project in the link provided on my website www.vmudunuru.com nk at V Link will be available from November 1, 2015 to submit your answers. The deadline to submit your project answers is November 27, 2015 by 11:59 PM. You can submit the project solutions only once. Please check your answers before you submit them. INSTRUCTIONS: Ve 1. Favorable Card Selection: In the Table-3 of this document there are 26 alphabet assigned with a unique cards from a deck of cards as their favorable event. Students whose LAST NAME starts with A are assigned with BLACK-ACE as their favorable event. Similarly students whose LAST NAME starts with N are assigned with RED-7 as their favorable event, and so on. 2. Give your answers in two decimal places for the probabilities calculated in this project. Do not use fractions. 3. Follow the hints to answer your questions. 4. You may only submit this project once! Please check your work before you submit it. 5. Your section number must be between 21 - 26 or between 41 - 46. Use only two digits to mention your section. For example 21 or 43, etc. First Name: Last Name: Section: UID (Starting with U): FALL 2015 STA 2023 PROJECT MUDUNURU, VENKATESWARA RAO 2 Experiment-1: Shuffle a deck of cards at least for 5 times and then lay out eight cards face up. Record the number of red cards or black cards according to your choice as given below in the Table-3. Reshuffle and lay out 8 cards again face up. Repeat this for 4 trials and fill the Table-1 with your observations in each trail and complete the Table with computing your probabilities in the third column of Table-1. Question-1: Based on your Last Name what is your favorable card for doing these nV experiments? {Hint: Black-A, Red-K, etc...} Question-2: If X is the random variable of drawing your favorable card, is X a discrete random variable or a continuous random variable? {Hint: Give your answer as Discrete or Continuous} nk at V Question-3: When drawing a card from the deck of cards, what is the probability of drawing your favorable card? Question-4: When you draw 8 cards out of the deck. What is the probability that we have exactly 4 of your favorable color (red or black) cards? Let # of Fav Colors denote the Observed Number of your Favorable color (Red or Black) Cards in each trial. Let # of Fav Card denote the Observed number of your Favorable card facing up in each trial. Let P(# of Fav Card |# of Fav Color) denote the Probability of your favorable card given that your favorable color showed up in each trial. Ve Question-5: Complete the Table-1 with your results. Table 1 for Experiment-1 Trials # of Fav Colors # of Fav Card P(# of Fav Card|# of Fav Colors) 1 2 3 4 FALL 2015 STA 2023 PROJECT MUDUNURU, VENKATESWARA RAO 3 Experiment-2: Perform the following action thrice, and record how many favorable outcomes occurred after performing these steps for three times. Your event is drawing a favorable card mentioned below in Table-2. Do this experiment for 10 times. Remember that performing three steps is considered as one trial. You should do this for 10 times. START STOP nk at V nV Step-1: Draw a card from a standard deck, and note if whether the card drawn is your favorable outcome or not. Place the card back in the deck. Step-2: Be sure to shuffle the deck, draw for second time, note if whether the card drawn is your favorable outcome or not. Place the card back in the deck. Step-3: Be sure to shuffle the deck again, draw for third time, note if whether the card drawn is your favorable outcome or not. Place the card back in the deck. Now shuffle again, repeat these 3 steps for 10 times. Note the results based on your favorable card or not. Then record how many favorable events you have got. Your results will look like 0, 3, 1, 0, 2, 0, 0... TEN values. Ve Remember your favorable event can happen only for one time in your three attempts, then record it as 1; OR if your favorable event can happen for two times in your three attempts, then record it as 2; OR if your favorable event can happen for all the three times in your three attempts, then record it as 3; OR it will not happen in all the three attempts, then record it as 0; Question-6: What will be your sample space in this experiment? [Note: Give your answer in { } with comma separation. [Hint: For example: {11,12,13}]] Question-7: List all your outcomes in order for this experiment? [Note: Give your answer in { } with comma separation. [Hint: For example: {1,0,0,2,0,3...}] Question-8: What is the probability of your respective favorable outcome? Question-9: Let X be the random variable that your favorable outcome can happen. FALL 2015 STA 2023 PROJECT MUDUNURU, VENKATESWARA RAO 4 Based on your results in doing this experiment-2, record your results in the following Table-2 Table 2 for Experiment-2 Frequency Probability of X nV X 0 1 2 3 Question-10: What graph can well explain your experiment? Histogram or Bell Curve? nk at V Question-11: What is the expected value for your favorable event to occur? Question-12: What is the variance of your favorable event to occur? Question-13: What is the standard deviation of your favorable event to occur? Question-14: Is the probability distribution in Table-1 a plausible or not. [Hint: Give your answer as Yes or No] Question-15: Is the probability distribution in Table-2 a plausible or not. [Hint: Give your answer as Yes or No] Question-16: Is the probability distribution in Table-3 a plausible or not. [Hint: Give your Ve answer as Yes or No] FALL 2015 STA 2023 PROJECT MUDUNURU, VENKATESWARA RAO 5 Table 3 Selection Table Card Choice ACE ACE 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 JACK JACK QUEEN QUEEN KING KING nV Card Color Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Black Red Ve nk at V Last Name Starting with A B C D E F G H I J K L M N O P Q R S T U V W X Y Z FALL 2015 STA 2023 PROJECT MUDUNURU, VENKATESWARA RAO