Events A1, A2 and Az form a partiton of the sample space S with probabilities P(A) = 0.2, P(A2) = 0.4, P(A3) = 0.4. If E is an event in S with P(E|A) = 0.5, P(E|A2) = 0.6, P(E|A3) = 0.7, compute %3D %3D P(E) = P(A||E) = P(A2|E) = %3D P(A3|E) = %3D
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- 8.3.153. If random variable X takes on the values of -1,0 and 2 with probabilities 0.3, 0.3, and 0.4 respectively, what is its expected value, E(X)?Select the THREE statements about probabilities and p-values given below which are TRUE. Select one or more: In hypothesis testing, a p-value of less than 0.0005 means there is very strong evidence against the null hypothesis. Suppose A and B are two statistically independent events. If P(A) = 0.3 and P(B) = 0.6 then P(A and B) must be equal to 0.18. If event A is more likely than event B, then P(A) is less than P(B). The value 0.42 is a valid value for a probability. The value 1.983 is a valid value for a p-value. If A and B are mutually exclusive events then P(A or B) must be equal to zero.
- Compute the z-scores and the population probabilities for these normally distributed events: a) mx = 96, sx = 14, z = _______ P(x < 81) = _____________ b) mx = 0.42, sx = 0.11, z = _______ P(x > 0.60) = _____________ c) mx = 1250, sx = 850, z = _______ P(x > 650) = _____________ d) mx = 9.0, sx = 3.4, z = _______ P(x < 11.8) = _____________A volunteer ambulance service handles 0 to 5 service calls on any given day. I hè pPoBablity distribution for the number of service calls is as follows: 1 2 3 4 f (x) 0.15 0.20 0.30 0.20 0.10 0.05 Based on this probability distribution: • The volunteer ambulance service has a chance of handling at least 3 calls on a particular day. • The most likely number of service calls that the volunteer ambulance will handle on a given day is calls. Note: Use the exact value of the mean in answering this question. Note: Input both of your answers rounded off to two decimal places.GROUP A: 2. The amount of the demand of deposits made daily in a certain banking agency, is random with normal distribution of average 120 currency units and variance 64. Determine: (a) the percentage of days on which the amount of demand deposits is between 105 and 135 currency units. (B) the probability that the amount of deposits is higher than the average, in the days when this amount is less than 125 currency units. wwwwwwwww (C) the average and variance of the amount of demand deposits made weekly (consider that a week has 5 days). (D) the lower limit of the amount of deposits which is 90% of the days.
- Bernoulli process: i.Draw the probability distributions (pdf) for X∼bin (8, p) (x) forp = 0.25, p = 0.5, p = 0.75, in each diagram.ii.What kind of effect has a higher value on the graph , compared to a lower value? iii.You should strike a coin8gonger. You win if there are precise4 or precise5 coins, but otherwise lose. You can choose between three different coins, medpn = P (coin) respectively p1 = 0.25, p2 = 0.5, andp3 = 0.75. Which of these coins gives you the highest probability of winning?1. In the experiment of tossing 3 coins, what is the probability of getting 3 heads? 2. The events x and y are mutually exclusive events. If P(x) = 0.4 and P(y) = 0.3, what is the probability of either x or y? What is the probability that neither x nor y will occur? %3D %3D 3. A student enrolled two math subjects: statistics and algebra. His chance of passing the statistics subject 0.65. His chance of passing algebra is 0.80 and his chance of passing both subjects is 0.50. What is the probability of passing at least one subject?3
- 1. The distributional pattern of pulmonate slugs inhabiting Libya was studied in the AIUB Journal of Science and Engineering (Aug. 2003). The number of slugs of a certain species found in the survey area was modeled using the negative binomial distribution. Assume that the probability of observing a slug of a certain species (say, Milax rusticus) in the survey area is 0.2. Let Y represent the number of slugs that must be collected in order to obtain a sample of 10 Milax rusticus slugs. a. Give the probability distribution for Y as a formula. b. What is the expected value of Y? Interpret this value.c. Find P(Y = 25).21:18 64 | 30ll a O 100 JO Imssb1.mutah.edu.jo/m Number of sales of household appliances, Y, makes in a day is given by following probability distribution. y: 3 4 p(y) : 0.10 0.28 0.18 0.11 0.16 0.17 Expected value of (2Y -3): Select one: а. 1.41 b. 1.45 c. 1.92 d. 2.46 e. None of These +3