MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Discrete Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A random variable X can take only two values, 2 and 4 i.e., P(2) = 0.45 and P(4) = 0.97. What is the Expected value of X? |
| A. | 3.8 |
| B. | 2.9 |
| C. | 4.78 |
| D. | 5.32 |
| Answer» D. 5.32 | |
| 2. |
A fair cubical die is thrown twice and their scores summed up. If the sum of the scores of upper side faces by throwing two times a die is an event. Find the Expected Value of that event. |
| A. | 48 |
| B. | 76 |
| C. | 7 |
| D. | 132 |
| Answer» D. 132 | |
| 3. |
A 6-sided die is biased. Now, the numbers one to four are equally likely to happen, but five and six is thrice as likely to land face up as each of the other numbers. If X is the number shown on the uppermost face, determine the expected value of X when 6 is shown on the uppermost face. |
| A. | \(\frac{13}{4}\) |
| B. | \(\frac{3}{5}\) |
| C. | \(\frac{2}{7}\) |
| D. | \(\frac{21}{87}\) |
| Answer» B. \(\frac{3}{5}\) | |
| 4. |
A Random Variable X can take only two values, 4 and 5 such that P(4) = 0.32 and P(5) = 0.47. Determine the Variance of X. |
| A. | 8.21 |
| B. | 12 |
| C. | 3.7 |
| D. | 4.8 |
| Answer» D. 4.8 | |
| 5. |
In a card game Reena wins 3 Rs. if she draws a king or a spade and 7 Rs. if a heart or a queen from an pack of 52 playing cards. If she pays a certain amount of money each time she will lose the game. What will be the amount so that the game will come out a fair game? |
| A. | 15 |
| B. | 6 |
| C. | 23 |
| D. | 2 |
| Answer» E. | |
| 6. |
A football player makes 75% of his 5-point shots and 25% his 7-point shots. Determine the expected value for a 7-point shot of the player. |
| A. | 4.59 |
| B. | 12.35 |
| C. | 5.25 |
| D. | 42.8 |
| Answer» D. 42.8 | |
| 7. |
Let X is denoted as the number of heads in three tosses of a coin. Determine the mean and variance for the random variable X. |
| A. | 4.8 |
| B. | 6 |
| C. | 3.2 |
| D. | 1.5 |
| Answer» E. | |
| 8. |
A probability density function f(x) for the continuous random variable X is denoted as _______ |
| A. | ∫ f(x)dx = ∞, -1<=x<=1 |
| B. | ∫ f(x)dx = 1, -∞<=x<=∞ |
| C. | ∫ f(x)dx = 0, -∞<=x<=∞ |
| D. | ∫ f(x+2)dx = .5, -∞<=x<=∞ |
| Answer» C. ∫ f(x)dx = 0, -∞<=x<=∞ | |
| 9. |
A jar of pickle is picked at random using a filling process in which an automatic machine is filling pickle jars with 2.5 kg of pickle in each jar. Due to few faults in the automatic process, the weight of a jar could vary from jar to jar in the range 1.7 kg to 2.9 kg excluding the latter. Let X denote the weight of a jar of pickle selected. Find the range of X. |
| A. | 3.7 ≤ X < 3.9 |
| B. | 1.6 ≤ X < 3.2 |
| C. | 1.7 ≤ X < 2.9 |
| D. | 1 ≤ X < 5 |
| Answer» D. 1 ≤ X < 5 | |
| 10. |
Two t-shirts are drawn at random in succession without replacement from a drawer containing 5 red t-shirts and 8 white t-shirts. Find the probabilities of all the possible outcomes. |
| A. | 1 |
| B. | 13 |
| C. | 40 |
| D. | 346 |
| Answer» B. 13 | |