<prompt> Fana ka mehlala e 3 ea mehlala ea bohlokoa.nan  <response>: Instruction in English: Give 3 examples of importance sampling. . Response in English: 1. Monte Carlo simulations: In situations where it is difficult to compute the expectation of a random variable analytically, Monte Carlo simulations can be used to estimate it through random sampling. However, when dealing with rare events or highly skewed distributions, it can be very inefficient to use standard random sampling, as it would take a lot of samples to obtain a good estimate. Importance sampling can be used in these cases to choose a sampling distribution that assigns more probability to the important regions, which can significantly reduce the number of samples required to obtain a good estimate.2. Variance Reduction in Computer Graphics: In computer graphics, Monte Carlo integration is used to estimate the light transport equation to create realistic images. However, the high variance of some Monte Carlo estimators can result in noisy images, especially in scenes with complex lighting interactions. Importance sampling can be used in this context to reduce the variance of the estimator by sampling the light sources according to their contribution to the final image, which can result in smoother images with less noise.3. Bayesian Inference: Importance sampling can be used in Bayesian inference to estimate the posterior distribution of model parameters when the likelihood function is difficult to evaluate. This is common in models with complex or high-dimensional likelihood functions, where computing the normalization constant of the posterior distribution can be challenging. By using importance sampling, it is possible to select a proposal distribution that approximates the shape of the posterior, which allows for efficient sampling of the important regions of the parameter space. . Response in Sesotho: 1. Lipapiso tsa Monte Carlo: Maemong ao ho leng thata ho lekanya tebello ea ho feto-fetoha ho sa tloaelehang ka tlhahlobo, lipapiso tsa Monte Carlo li ka sebelisoa ho lekanya ka sampuli e sa reroang. Leha ho le joalo, ha ho sebetsanoa le liketsahalo tse sa tloaelehang kapa kabo e sothehileng haholo, ho ka ba thata haholo ho sebelisa lisampole tse tloaelehileng, kaha ho ka nka lisampole tse ngata ho fumana khakanyo e ntle. Mehlala ea bohlokoa e ka sebelisoa maemong ana ho khetha kabo ea lisampole e fanang ka monyetla o eketsehileng ho libaka tsa bohlokoa, tse ka fokotsang haholo palo ea lisampole tse hlokahalang ho fumana khakanyo e ntle. 2. Phapang ea Phokotso ea Litšoantšo tsa Khomphuta: Litšoantšong tsa khomphieutha, ho kopanya ha Monte Carlo ho sebelisoa ho hakanya palo ea lipalangoang tse bobebe ho etsa litšoantšo tsa sebele. Leha ho le joalo, phapang e phahameng ea likhakanyo tse ling tsa Monte Carlo e ka fella ka litšoantšo tse lerata, haholo-holo litšoantšong tse nang le likamano tse rarahaneng tsa mabone. Mehlala ea bohlokoa e ka sebelisoa moelelong ona ho fokotsa phapang ea likhakanyo ka ho etsa sampole mehloli ea leseli ho latela tlatsetso ea bona setšoantšong sa ho qetela, e leng se ka fellang ka litšoantšo tse thellang tse nang le lerata le fokolang. 3. Boikemisetso ba Bayesian: Sampling ea bohlokoa e ka sebelisoa mohopolong oa Bayesian ho hakanya kabo ea morao-rao ea liparamente tsa mohlala ha mosebetsi oa monyetla o le thata ho o hlahloba. Sena se tloaelehile mefuteng e nang le tsebetso e rarahaneng kapa e phahameng-dimensional, moo computing the normalization constantization of posterior distribution e ka bang phephetso. Ka ho sebelisa sampling ea bohlokoa, hoa khoneha ho khetha kabo ea tlhahiso e lekanang le sebopeho sa morao, e leng se lumellang ho etsa sampling e sebetsang hantle ea libaka tsa bohlokoa tsa sebaka sa parameter. 