Note: i) Attempt TWO Questions in all, by selecting ONE question from each section. ii) FOUR marks are reserved for PRACTICAL NOTE BOOK and FIVE for VIVA VOCE.

**1. **The following are the prices of 5 commodities for the years 1946 to 1953.

Year | Commodities | |||||
---|---|---|---|---|---|---|

A | B | C | D | E | ||

1946 | 87.25 | 66 | 18.50 | 21.12 | 42.12 | |

1947 | 82.50 | 69 | 19.25 | 25.12 | 45.37 | |

1948 | 82.37 | 54 | 17.75 | 18.12 | 50.12 | |

1949 | 81.87 | 78 | 18.12 | 15.12 | 60.19 | |

1950 | 82.50 | 69 | 19.13 | 20.50 | 65.25 | |

1951 | 83.75 | 81 | 20.37 | 25.25 | 55.12 | |

1952 | 89.50 | 85 | 24.37 | 26.12 | 66.50 | |

1953 | 95.00 | 102 | 22.50 | 26.25 | 70.31 |

Construct Price Index Number by chain base method taking 1946 as base and using geometric mean as average.

**2. **Compute Seasonal indices by link relative method using median as average Also deseasonalize the data for 3^{rd }week. *7+1 *

Week | Days | |||||
---|---|---|---|---|---|---|

Sat. | Sun | Mon. | Tue. | Wed. | Thur. | |

1 | 128 | 95 | 89 | 75 | 82 | 107 |

2 | 137 | 98 | 85 | 79 | 80 | 105 |

3 | 130 | 96 | 87 | 78 | 85 | 108 |

4 | 132 | 100 | 88 | 80 | 84 | 110 |

5 | 135 | 102 | 90 | 82 | 86 | 112 |

6 | 136 | 103 | 92 | 80 | 89 | 115 |

**3 . From a well shuffled ordinary deck of 52 playing cards, 13 cards are selected without replacement.Determine probability distribution of number of heart cards. Find mean and variance of this distribution. Verify that: **

**n**K nK N-n)

N-K)

N N

i)e(x)= ii)Var(x)= K *4,2, 2 *

K

N N N-1

~~N ~~(

(

**4 . Fit a poisson distribution to the data given below: **

Mistake per Page | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

No. of Pages | 1006 | 2098 | 292 | 97 | 56 | 27 | 16 | 13 | 12 | 11 | 9 | 7 |

_{*** }B.A/B.Sc-I (09/A) P-vi_{*** }