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CONTENT DISCUSSION: (For Self-Paced Learning) If you have queries or questions regarding the content provided, please feel free to consult or message the subject teacher through messenger, text, call, or video chat) Day 1: Properties of a discrete probability Distribution A 2 12ITAT2 : mojdn2 Examine the probability distribution that we have obtained in the given example (banana) What do you notice about the probability values of the random variable in each probability distribution? What is the sum of the probabilities of a random variable? Example: Consider the probability distribution of the number of bananas given below. "j' info ) R 3 2 0 P(R) 178 3/8 3/8 1/8 Find the following: POSSIBLE ANSWER 6. P(R=3) 1/8 7. P(R=1) 3/8 8. P(R>1) P(2)+ P(3) = 3/8+1/8=1/2 9. P(R [X . P(X)] = 1/2 +1/2 + 0 1(X)9 . X13 = (X)3 = 4 = 1 0+ 8:8 + 810 + 818 = a. I = Step 2: Square each value of the random variable and multiply by the corresponding probability value [ X2 . P (X) ]. The table below will be helpful. P(X) X' . P(X) vint to from ords bail 1/2 1/2 0 0 or.0 OS.0 Step 3. Find the variance and the standard deviation by applying the formulas E A 02 = [[x2 . P(X)] - 142 S (1)9 . A b ( B ) A =(1+ 1/2+0)-12 OIVE =1/2 ~ 0.5 The standard deviation is computed by getting the square root of the variance. 0 = [ (x2 . P(X)] - 12 = V0.5 =0.707 andi dilw 7. old Thus, the variance is 0.5 and the standard deviation is 0.707 s) push BV edT .Boiluditeib ylidedone goiwollor 13ACTIVITY 1: Suppose that the number of car accidents per day in Torrance, CA has been recorded'for the past year. The table below is a probability distribution table representing the data collected. ' ' ' a 1 . I Number of accidents per day -___ probability m a. What is the probability that on a given day, the number of accidents will be 4? b. On any given day, how many accidents do you expect to have? c. What is the probability that on a given day, the number of accidents is less than 3? ACTIVITY 2: Find the variance and the standard deviation of the following probability distributions. Complete the following tables. ACTIVITY 3: Find the mean, variance and the standard deviation of the following probability distributions. . BYBOXTV evoulf mi?. lob xnowCl X P (X) 0.238 IN 0.290 0.177 UI A W 0.158 NANVITOA 0.137 ACTIVITY 4: HID YTLIBAMONG CHA PDITEITATE X P (X) 0.103 0.118 0.246 aUAWNHO 0.229 0.138 0.094 0.071 J 0.001 S EL.O 25.0 Shed thew atmsbrass lo edmon add yob nmag . no ford vidsdora an al isty