Suppose three marksmen shoot at a target. The ith marksman fires ni times, hitting the target each time with probability Pi, independently of his other shots and the shots of the other marksmen. Let X be the total number of times the target is hit.Is this distribution binomial?

Distribution is NOT binomial.

Step-by-step explanation:

In order to be a binomial distribution, the probability of success for each individual trial must be the same. Since each marksman hits the target with probability Pi, the probability of success (hitting the target) is not necessarily equal for all trials. Therefore, the distribution is not binomial.

In this case, the distribution would only be binomial if Pi was the same for every "ith" marksman.

Native American Indians were the major source of beaver pelts and buffalo hides, for the Canadian, Great Lakes, and upper Missouri River fur trade. Until the early 19th century, Native Americans used nets, snares, deadfalls, clubs, etc. to obtain beaver pelts. By the late seventeen hundreds, the Plains Indians were exchanging beaver pelts and horses to the Hudson’s Bay and North West fur traders for European goods on the Kootenae Plains and at the Missouri River trade fairs. The Missouri River trade fairs were held at the villages of the Mandan, Hidatsa, and Arikara Indians. Exchanged at the trade fairs were garden products (beans, squash, corn, etc.) raised at the Missouri River villages, horses, furs, and hides from the Plains Indians, and whiskey, guns, iron goods, trade beads, and a few beaver traps from the North West traders. The North West trader François-Antoine Larocque took beaver traps to the Crow in 1805.

In the Mountain Man and Native American Fur Trade articles, the Plains Indians and Indians of the Rocky Mountain area are grouped together as Plains Indians.

Plains Indians

Major Indian tribes of the Fur Trade

Ethnologists considered the nomadic tribes as the Plains Indians–not the semi-sedentary tribes like the Mandan, Arikara and Hidatsa.

The Fur  Trappers:

Building a fur trading post at the junction of the Bighorn and Yellowstone rivers changed the economic dynamics of the Plains Indian fur trade. Fort Raymond (Fort Ramon, Fort Lisa) was built by Manuel Lisa in 1807. Named after Lisa’s son, Fort Raymond was the first American fur trading post in the Rocky Mountains–David Thompson had built Kootenae House a few months earlier in British Columbia. From this post, Lisa sent John Colter, George Drouillard, and Edward Rose to Crow Indian villages to inform them of a the trading post.

The Lisa, Menard, and Morrison Fur Company employed trappers to trap and trade with individual tribes. This curtailed a “fur trade fair” system in existence for decades. It can be argued Americans trading directly with Native American Indian tribes was a major factor in the hostility of the Blackfeet, Arikara, and Sioux toward the Mountain Men. The Blackfoot and the Sioux did not want the Americans trading with their enemies, or in the case of the Blackfeet trapping their territory. The Blackfeet traded for guns with the North West Company in Canada, as did the Sioux with North West traders on the James River. The Blackfeet and Sioux did not want Americans trading guns to the other Indian tribes along the Missouri River. The Arikara opposed the white man because they did not want to lose their role as middle men in the Plains Indian trade fair system.

The Lisa, Menard, and Morrison Fur Company is also credited with building a trading post at the Three Forks in Montana, but this is questionable–to the Mountain Man a fort was usually a log barricade. The fur trappers arrived at the Three Forks on April 3, 1810, and a trapping party was attacked on April 12th. Five trappers were killed. The rest of the party forted up behind a log barricade. Tired of staying behind the barricade, George Drouillard and two Delaware Indians went up the Gallatin River to trap where they were killed by the Blackfeet.

After the loss of eight men, their guns, traps, and seven horses, Pierre Menard took part of the trappers back to Fort Raymond. Andrew Henry stayed at the Three Forks with sixty men, but by fall, he and his men had abandoned the area. If Henry and his men were continuously harassed by the Blackfeet, when did they have time to cut and haul logs to build a fort? If a fort was built, why abandon it before the start of the fall trapping season when the pressure from the Blackfeet may lessen. By in large, Indians did not send out large war parties in the winter time. In September, Henry’s men crossed the Continental Divide, and spent the winter on Henry’s Fork of the Snake River.

The Arikara battle in 1823 forced the Ashley-Henry Fur Company to abandon the Missouri River. In 1825, Ashley took at pack train overland to the first Mountain Man Rendezvous. The Rendezvous System lasted from 1825 to 1840. Six of the rendezvous were held on Horse Creek in the Green River Valley of Wyoming.

This old beaver house and dam is not far from where Mill Creek empties into the North Fork of Horse Creek. The beaver dam pictures on the Mountain Man-Indian Fur Trade site are about twenty-five miles west of the Mountain Man Horse Creek Rendezvous sites of 1833, 1835, 1836, 1837, 1839, and the last one in 1840.

Explanation: