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| ๐ Question (with marks) | ๐ Exam References | ๐ PDF Links |
|---|---|---|
| ๐ TOPIC: Basic Probability, Conditional Probability & Bayes' Theorem | ||
| Shaft A and B are tested independently. P(A conforms)=1/7, P(B conforms)=1/5. Find i) both conform ii) exactly one conforms iii) at least one conforms. [06] ๐ฅ High Yield๐งฎ Numerical | Apr 25 Dec 24 Jun 23 | ๐ Course Pg 244 ๐ Exam Pg 1 |
| Medical symptoms: illnesses A,B,C with prior probabilities 0.01,0.005,0.02. Symptom H probabilities 0.90,0.95,0.75. If a person shows H, find P(illness A). [06] ๐ฅ High Yield๐ Bayes | Apr 25 Dec 23 Aug 23 | ๐ Course Pg 286 ๐ Exam Pg 34 |
| Random arrangement of letters of "INDEPENDENCE". Probability that all vowels are together. [06] ๐น Rare๐ Permutation | Apr 24 Jun 23 | ๐ Course Pg 262 ๐ Exam Pg 34 |
| ๐ TOPIC: Discrete & Continuous Random Variables (PMF, PDF, Expectation) | ||
| The probability mass function: X=0..6 with p(x)=k,0.12,0.25,0.188,k,0.14,0.06. Find k, mean, variance. [06] ๐ฅ High Yield๐งฎ Expectation | Apr 25 Dec 24 Feb 24 | ๐ Course Pg 309 ๐ Exam Pg 2 |
| Continuous random variable X with p.d.f. f(x)=k(1+x), 2โคxโค5. Find P(X<4). [06] ๐งฎ PDF | Dec 23 Apr 24 | ๐ Course Pg 303 ๐ Exam Pg 22 |
| ๐ Question (with marks) | ๐ Exam References | ๐ PDF Links |
|---|---|---|
| ๐ฏ TOPIC: Binomial Distribution | ||
| Four cards drawn from a wellโshuffled pack without replacement. Probability that (i) all are diamonds (ii) one card of each suit (iii) two spades and two hearts. [06] ๐ฅ High Yield๐งฎ Combination | Apr 25 Dec 23 Jun 24 | ๐ Course Pg 327 ๐ Exam Pg 30 |
| A speaks truth 70%, B 85%. Find percentage of cases they contradict each other stating same fact. [06] ๐ฅ High Yield๐ Probability | Apr 25 Dec 24 Feb 23 | ๐ Course Pg 325 ๐ Exam Pg 18 |
| ๐ TOPIC: Poisson Distribution (Rare events) | ||
| In a batch of 5000 components, 100 are defective. A box of 100 components is selected. Using Poisson approximation, find i) P(at most 3 defective) ii) P(at least 2 defective) iii) P(between 2 and 5 inclusive). [07] ๐ฅ High Yield๐งฎ Poisson | Apr 25 Dec 24 Jun 23 | ๐ Course Pg 340 ๐ Exam Pg 2 |
| A manufacturer of medicine bottles finds 0.1% defective. Bottles packed in boxes of 500. A drug manufacturer buys 100 boxes. Find how many boxes contain (i) no defectives (ii) at least two defectives. [07] ๐ Long๐งฎ Poisson | Apr 25 Dec 24 | ๐ Course Pg 350 ๐ Exam Pg 35 |
| ๐ TOPIC: Normal Distribution & Applications | ||
| Wait times at driveโthrough: normal with mean 185 sec, ฯ=15 sec. Find percentage of wait times i) between 155 and 215 sec ii) more than 170 sec iii) less than 155 sec. [07] ๐ฅ High Yield๐งฎ Zโtable | Apr 25 Dec 24 Jun 23 | ๐ Course Pg 364 ๐ Exam Pg 3 |
| Life of electronic device: mean 300 hours, ฯ=25 hours. (i) probability life more than 350 hours (ii) percentage between 220 and 260 hours. [07] ๐งฎ Normal | Dec 23 Apr 25 | ๐ Course Pg 378 ๐ Exam Pg 8 |
| ๐ Question (with marks) | ๐ Exam References | ๐ PDF Links |
|---|---|---|
| ๐ TOPIC: Karl Pearsonโs Correlation Coefficient | ||
| A computer calculated correlation with n=30, ฮฃX=120, ฮฃXยฒ=600, ฮฃY=90, ฮฃYยฒ=250, ฮฃXY=335 but two pairs were wrong: (8,10) and (12,7) should be (8,12) and (10,8). Find the correct value of r. [06] ๐ฅ High Yield๐งฎ Correction | Apr 25 Dec 24 Jun 24 | ๐ Course Pg 117 ๐ Exam Pg 4 |
| From the following data calculate Karl Pearsonโs coefficient: x: 17,19,21,26,20,28,26,27 ; y: 23,27,25,26,27,25,30,33. [06] ๐ Long๐งฎ Correlation | Feb 24 Dec 23 | ๐ Course Pg 108 ๐ Exam Pg 23 |
| ๐ TOPIC: Spearmanโs Rank Correlation | ||
| Ten students thesis marks by two judges: Judge1: 26,28,18,26,22,26,18,20,21,29 ; Judge2: 25,22,22,25,22,28,22,23,24,27. Compute Spearmanโs rank correlation coefficient. [06] ๐ Rank | Apr 25 Dec 24 | ๐ Course Pg 133 ๐ Exam Pg 3 |
| ๐ TOPIC: Regression Lines & Coefficients | ||
| Regression lines: 40xโ18yโ214=0 and 8xโ10y+66=0. Find mean(x), mean(y), correlation coefficient, and estimate x when y=20. [06] ๐ฅ High Yield๐งฎ Regression | Apr 25 Dec 24 Jun 23 | ๐ Course Pg 196 ๐ Exam Pg 3 |
| Find regression lines and estimate y when x=66, x when y=74 from data: x:57,58,59,59,60,61,62,64 ; y:67,68,65,68,72,72,69,71. [07] ๐ Long๐งฎ Linear regression | Dec 23 Apr 24 | ๐ Course Pg 199 ๐ Exam Pg 20 |
| ๐ Question (with marks) | ๐ Exam References | ๐ PDF Links |
|---|---|---|
| ๐ TOPIC: Least Squares โ Power & Exponential Curves | ||
| Fit a curve of the form y = aยทx^b to the data: x:2,4,6,8,10,12,20,25 ; y:40,320,1080,2560,5000,8640,40000,78125. Estimate y when x=9.5. [06] ๐งฎ Power curve | Apr 25 Dec 24 | ๐ Course Pg 235 ๐ Exam Pg 3 |
| Fit exponential curve y = aยทb^x by least squares to: x:1,2,3,4,5 ; y:7.12,7.86,2.11,10,161 (data approximate). [06] ๐น Rare๐ Exponential | Feb 24 Apr 25 | ๐ Course Pg 230 ๐ Exam Pg 36 |
| ๐ TOPIC: Median, Mode & Standard Deviation (Grouped Data) | ||
| From grouped frequency table (marks 0-12 to 108-120 with frequencies: 2,2,3,5,21,44,35,56,32,45,42,57), compute median and modal marks. [06] ๐ฅ High Yield๐งฎ Central tendency | Apr 25 Dec 24 Jun 23 | ๐ Course Pg 25 ๐ Exam Pg 3 |
| Compute standard deviation for IQ of 50 boys: classes 0-20,20-40,...,140-160 with frequencies 3,4,3,4,13,12,8,3. [06] ๐ Dispersion | Dec 23 Apr 24 | ๐ Course Pg 58 ๐ Exam Pg 8 |
| ๐ Question (with marks) | ๐ Exam References | ๐ PDF Links |
|---|---|---|
| ๐ TOPIC: OneโSample Zโtest (Mean & Proportion) | ||
| Last year proportion of defective items 0.022. This year sample of 250 items, 7 defective. Test if proportion has changed (ฮฑ=0.05). Find pโvalue. [07] ๐ฅ High Yield๐งฎ Proportion test | Apr 25 Dec 24 Feb 24 | ๐ Course Pg 428 ๐ Exam Pg 4 |
| Packaging machine set to mean weight 5 kg, ฯ=0.21 kg. Sample of 100 packets mean = 5.03 kg. Can we conclude mean weight has increased? Use 5% level. [07] ๐ฅ High Yield๐งฎ Zโtest | Apr 25 Dec 24 Jun 23 | ๐ Course Pg 419 ๐ Exam Pg 9 |
| ๐ TOPIC: tโtest for Small Samples (ฯ unknown) | ||
| Farmer claims yield >14 quintals. Sample yields: 14.3,12.6,13.7,10.9,13.7,12.0,11.4,12.0,13.0,12.8. Test the claim at 5% significance level. [07] ๐ Long๐งฎ Oneโsample t | Apr 25 Dec 24 | ๐ Course Pg 450 ๐ Exam Pg 4 |
| A machine designed to produce washers of average thickness 0.025 cm. Sample of 10 washers: mean 0.024 cm, s=0.002 cm. Test significance of deviation at 5% level. [07] ๐งฎ tโtest | Dec 24 Apr 25 | ๐ Course Pg 450 ๐ Exam Pg 36 |
| ๐ญ TOPIC: TwoโSample & Variance Tests | ||
| Sample of 100 iron bars mean length 4.2 ft, population mean 4 ft, ฯ=0.5 ft. Can the sample be regarded as truly random at 5% significance level? [07] ๐น Rare๐งฎ Zโtest | Apr 24 Dec 23 | ๐ Course Pg 426 ๐ Exam Pg 36 |
| ๐ฆ TOPIC: Poisson & Normal Approximations | ||
| Microchips: 5% defective. Box of 1000, guarantee not more than 10 defective. Approximate probability that a box fails the guarantee using Poisson approximation. [07] ๐ Long๐งฎ Poisson | Dec 23 Apr 24 | ๐ Course Pg 351 ๐ Exam Pg 19 |
| 1000 light bulbs, mean life 120 days, ฯ=20 days, normally distributed. How many bulbs expire in less than 90 days? Between 110 and 125 days? [07] ๐งฎ Normal | Apr 25 Dec 24 | ๐ Course Pg 378 ๐ Exam Pg 35 |
| โ๏ธ TOPIC: Curve Fitting (Polynomial) | ||
| Fit secondโdegree parabola y = a + bx + cxยฒ to data: x:0,1,2,3,4 ; y:1,3,4,5,6 using least squares. [07] ๐ Polynomial | Apr 24 Dec 23 | ๐ Course Pg 208 ๐ Exam Pg 20 |